We classify nonabelian extensions of Lie algebroids in the holomorphic or algebraic category, and introduce and study a spectral sequence that one can attach to any such extension and generalizes the Hochschild-Serre spectral sequence associated to an ideal in a Lie algebra. We compute the differentials of the spectral sequence up to $d_2$

10aLie algebroids, nonabelian extensions, spectral sequences1 aBruzzo, Ugo1 aMencattini, Igor1 aTortella, Pietro1 aRubtsov, Vladimir uhttps://www.math.sissa.it/publication/nonabelian-lie-algebroid-extensions00812nas a2200133 4500008004100000245006300041210006200104260003000166520036300196100001600559700002600575700002600601856005100627 2013 en d00aSymplectic instanton bundles on P3 and 't Hooft instantons0 aSymplectic instanton bundles on P3 and t Hooft instantons barXiv:1312.5554 [math.AG]3 aWe introduce the notion of tame symplectic instantons by excluding a kind of pathological monads and show that the locus $I^*_{n,r}$ of tame symplectic instantons is irreducible and has the expected dimension, equal to $4n(r+1)-r(2r+1)$. The proof is inherently based on a relation between the spaces $I^*_{n,r}$ and the moduli spaces of 't Hooft instantons.1 aBruzzo, Ugo1 aMarkushevich, Dimitri1 aTikhomirov, Alexander uhttp://urania.sissa.it/xmlui/handle/1963/3448600646nas a2200133 4500008004100000245005800041210005500099260001300154520025200167653001900419100001600438700002200454856003600476 2012 en d00aOn localization in holomorphic equivariant cohomology0 alocalization in holomorphic equivariant cohomology bSpringer3 aWe prove a localization formula for a "holomorphic equivariant cohomology" attached to the Atiyah algebroid of an equivariant holomorphic vector bundle. This generalizes Feng-Ma, Carrell-Liebermann, Baum-Bott and K. Liu's localization formulas.10aLie algebroids1 aBruzzo, Ugo1 aRubtsov, Vladimir uhttp://hdl.handle.net/1963/658400979nas a2200133 4500008004100000245010200041210006900143260001000212520051900222100001600741700002600757700002600783856003600809 2012 en d00aModuli of symplectic instanton vector bundles of higher rank on projective space $\\mathbb{P}^3$0 aModuli of symplectic instanton vector bundles of higher rank on bSISSA3 aSymplectic instanton vector bundles on the projective space $\\mathbb{P}^3$ constitute a natural generalization of mathematical instantons of rank 2. We study the moduli space $I_{n,r}$ of rank-$2r$ symplectic instanton vector bundles on $\\mathbb{P}^3$ with $r\\ge2$ and second Chern class $n\\ge r,\\ n\\equiv r({\\rm mod}2)$. We give an explicit construction of an irreducible component $I^*_{n,r}$ of this space for each such value of $n$ and show that $I^*_{n,r}$ has the expected dimension $4n(r+1)-r(2r+1)$.1 aBruzzo, Ugo1 aMarkushevich, Dimitri1 aTikhomirov, Alexander uhttp://hdl.handle.net/1963/465601229nas a2200169 4500008004100000245006500041210006200106260001000168520073800178100001600916700003100932700001500963700001200978700001400990700001901004856003601023 2011 en d00aD-branes, surface operators, and ADHM quiver representations0 aDbranes surface operators and ADHM quiver representations bSISSA3 aA supersymmetric quantum mechanical model is constructed for BPS states bound to surface operators in five dimensional SU(r) gauge theories using D-brane engineering. This model represents the effective action of a certain D2-brane configuration, and is naturally obtained by dimensional reduction of a quiver $(0,2)$ gauged linear sigma model. In a special stability chamber, the resulting moduli space of quiver representations is shown to be smooth and isomorphic to a moduli space of framed quotients on the projective plane. A precise conjecture relating a K-theoretic partition function of this moduli space to refined open string invariants of toric lagrangian branes is formulated for conifold and local P^1 x P^1 geometries.1 aBruzzo, Ugo1 aDiaconescu, Duiliu-Emanuel1 aYardim, M.1 aPan, G.1 aZhang, Yi1 aWu-yen, Chuang uhttp://hdl.handle.net/1963/413300395nas a2200109 4500008004300000245008700043210006900130260001300199100002100212700001600233856003600249 2011 en_Ud 00aHolomorphic Cartan geometry on manifolds with numerically effective tangent bundle0 aHolomorphic Cartan geometry on manifolds with numerically effect bElsevier1 aBiswas, Indranil1 aBruzzo, Ugo uhttp://hdl.handle.net/1963/383000841nas a2200121 4500008004100000245005200041210005200093260002600145520047000171100001600641700002600657856003600683 2011 en d00aModuli of framed sheaves on projective surfaces0 aModuli of framed sheaves on projective surfaces bDocumenta Mathematica3 aWe show that there exists a fine moduli space for torsion-free sheaves on a\\r\\nprojective surface, which have a \\\"good framing\\\" on a big and nef divisor. This\\r\\nmoduli space is a quasi-projective scheme. This is accomplished by showing that such framed sheaves may be considered as stable pairs in the sense of\\r\\nHuybrechts and Lehn. We characterize the obstruction to the smoothness of the moduli space, and discuss some examples on rational surfaces.1 aBruzzo, Ugo1 aMarkushevich, Dimitri uhttp://hdl.handle.net/1963/512601388nas a2200157 4500008004300000245009200043210007000135260002200205300001200227490000800239520088500247100001601132700002201148700002401170856003601194 2011 en_Ud 00aPoincaré polynomial of moduli spaces of framed sheaves on (stacky) Hirzebruch surfaces0 aPoincaré polynomial of moduli spaces of framed sheaves on stacky bSpringerc06/2011 a395-4090 v3043 aWe perform a study of the moduli space of framed torsion-free sheaves on Hirzebruch surfaces by using localization techniques. We discuss some general properties of this moduli space by studying it in the framework of Huybrechts-Lehn theory of framed modules. We classify the fixed points under a toric action on the moduli space, and use this to compute the Poincare polynomial of the latter. This will imply that the moduli spaces we are considering are irreducible. We also consider fractional first Chern classes, which means that we are extending our computation to a stacky deformation of a Hirzebruch surface. From the physical viewpoint, our results provide the partition function of N=4 Vafa-Witten theory on total spaces of line bundles on P1, which is relevant in black hole entropy counting problems according to a conjecture due to Ooguri, Strominger and Vafa.

1 aBruzzo, Ugo1 aPoghossian, Rubik1 aTanzini, Alessandro uhttp://hdl.handle.net/1963/373800609nas a2200121 4500008004100000245003000041210002900071260001000100520030300110100001600413700002200429856003600451 2011 en d00aQ-factorial Laurent rings0 aQfactorial Laurent rings bSISSA3 aDolgachev proved that, for any field k, the ring naturally associated to a\\r\\ngeneric Laurent polynomial in d variables, $d \\\\geq 4$, is factorial. We prove a\\r\\nsufficient condition for the ring associated to a very general complex Laurent\\r\\npolynomial in d=3 variables to be Q-factorial.1 aBruzzo, Ugo1 aGrassi, Antonella uhttp://hdl.handle.net/1963/418301465nas a2200121 4500008004300000245006700043210006500110260001300175520107800188100001601266700002501282856003601307 2011 en_Ud 00aSemistable and numerically effective principal (Higgs) bundles0 aSemistable and numerically effective principal Higgs bundles bElsevier3 aWe study Miyaoka-type semistability criteria for principal Higgs G-bundles E on complex projective manifolds of any dimension. We prove that E has the property of being semistable after pullback to any projective curve if and only if certain line bundles, obtained from some characters of the parabolic subgroups of G, are numerically effective. One also proves that these conditions are met for semistable principal Higgs bundles whose adjoint bundle has vanishing second Chern class.\\r\\n\\r\\nIn a second part of the paper, we introduce notions of numerical effectiveness and numerical flatness for principal (Higgs) bundles, discussing their main properties. For (non-Higgs) principal bundles, we show that a numerically flat principal bundle admits a reduction to a Levi factor which has a flat Hermitian–Yang–Mills connection, and, as a consequence, that the cohomology ring of a numerically flat principal bundle with coefficients in R is trivial. To our knowledge this notion of numerical effectiveness is new even in the case of (non-Higgs) principal bundles.1 aBruzzo, Ugo1 aGrana-Otero, Beatriz uhttp://hdl.handle.net/1963/363800560nas a2200109 4500008004300000245005000043210004900093520023400142100001600376700002200392856003600414 2010 en_Ud 00aCohomology of Skew-holomorphic lie algebroids0 aCohomology of Skewholomorphic lie algebroids3 aWe introduce the notion of skew-holomorphic Lie algebroid on a complex manifold, and explore some cohomologies theories that one can associate to it. Examples are given in terms of holomorphic Poisson structures of various sorts.1 aBruzzo, Ugo1 aRubtsov, Vladimir uhttp://hdl.handle.net/1963/385300792nas a2200109 4500008004300000245004300043210004200086260005400128520044800182100001600630856003600646 2010 en_Ud 00aGauge theory: from physics to geometry0 aGauge theory from physics to geometry bIstituto di matematica. Universita\\\' di Trieste3 aMaxwell theory may be regarded as a prototype of gauge theory and generalized to nonabelian gauge theory. We briey sketch the history of the gauge theories, from Maxwell to Yang-Mills theory, and the identification of gauge fields with connections on fibre bundles. We introduce the notion of instanton and consider the moduli spaces of such objects. Finally, we discuss some modern techniques for studying the topology of these moduli spaces.1 aBruzzo, Ugo uhttp://hdl.handle.net/1963/410500671nas a2200109 4500008004300000245005300043210005300096520033800149100001600487700002200503856003600525 2010 en_Ud 00aPicard group of hypersurfaces in toric varieties0 aPicard group of hypersurfaces in toric varieties3 aWe show that the usual sufficient criterion for a generic hypersurface in a smooth projective manifold to have the same Picard number as the ambient variety can be generalized to hypersurfaces in complete simplicial toric varieties. This sufficient condition is always satisfied by generic K3 surfaces embedded in Fano toric 3-folds.1 aBruzzo, Ugo1 aGrassi, Antonella uhttp://hdl.handle.net/1963/410301102nas a2200109 4500008004300000245007400043210006900117520073300186100002100919700001600940856003600956 2010 en_Ud 00aOn semistable principal bundles over complex projective manifolds, II0 asemistable principal bundles over complex projective manifolds I3 aLet (X, \\\\omega) be a compact connected Kaehler manifold of complex dimension d and E_G a holomorphic principal G-bundle on X, where G is a connected reductive linear algebraic group defined over C. Let Z (G) denote the center of G. We prove that the following three statements are equivalent: (1) There is a parabolic subgroup P of G and a holomorphic reduction of the structure group of E_G to P (say, E_P) such that the bundle obtained by extending the structure group of E_P to L(P)/Z(G) (where L(P) is the Levi quotient of P) admits a flat connection; (2) The adjoint vector bundle ad(E_G) is numerically flat; (3) The principal G-bundle E_G is pseudostable, and the degree of the charateristic class c_2(ad(E_G) is zero.1 aBiswas, Indranil1 aBruzzo, Ugo uhttp://hdl.handle.net/1963/340401011nas a2200121 4500008004300000245008300043210006900126520059000195100001600785700002600801700002600827856003600853 2010 en_Ud 00aUhlenbeck-Donaldson compactification for framed sheaves on projective surfaces0 aUhlenbeckDonaldson compactification for framed sheaves on projec3 aWe construct a compactification $M^{\\\\mu ss}$ of the Uhlenbeck-Donaldson type for the moduli space of slope stable framed bundles. This is a kind of a moduli space of slope semistable framed sheaves. We show that there exists a projective morphism $\\\\gamma \\\\colon M^s \\\\to M^{\\\\mu ss}$, where $M^s$ is the moduli space of S-equivalence classes of Gieseker-semistable framed sheaves. The space $M^{\\\\mu ss}$ has a natural set-theoretic stratification which allows one, via a Hitchin-Kobayashi correspondence, to compare it with the moduli spaces of framed ideal instantons.1 aBruzzo, Ugo1 aMarkushevich, Dimitri1 aTikhomirov, Alexander uhttp://hdl.handle.net/1963/404900760nas a2200145 4500008004300000020002200043245006300065210006300128520031500191100001600506700001700522700001700539700002200556856003600578 2009 en_Ud a978-981-270-377-400aEquivariant cohomology and localization for Lie algebroids0 aEquivariant cohomology and localization for Lie algebroids3 aLet M be a manifold carrying the action of a Lie group G, and A a Lie algebroid on M equipped with a compatible infinitesimal G-action. Out of these data we construct an equivariant Lie algebroid cohomology and prove for compact G a related localization formula. As an application we prove a Bott-type formula.1 aBruzzo, Ugo1 aCirio, Lucio1 aRossi, Paolo1 aRubtsov, Vladimir uhttp://hdl.handle.net/1963/172400361nas a2200097 4500008004300000245007700043210006900120100001600189700002200205856003600227 2009 en_Ud 00aHolomorphic equivariant cohomology of Atiyah algebroids and localization0 aHolomorphic equivariant cohomology of Atiyah algebroids and loca1 aBruzzo, Ugo1 aRubtsov, Vladimir uhttp://hdl.handle.net/1963/377400891nas a2200121 4500008004300000245004600043210004600089520053600135100001600671700002200687700002400709856003600733 2008 en_Ud 00aInstanton counting on Hirzebruch surfaces0 aInstanton counting on Hirzebruch surfaces3 aWe perform a study of the moduli space of framed torsion free sheaves on Hirzebruch surfaces by using localization techniques. After discussing general properties of this moduli space, we classify its fixed points under the appropriate toric action and compute its Poincare\\\' polynomial. From the physical viewpoint, our results provide the partition function of N=4 Vafa-Witten theory on Hirzebruch surfaces, which is relevant in black hole entropy counting problems according to a conjecture due to Ooguri, Strominger and Vafa.1 aBruzzo, Ugo1 aPoghossian, Rubik1 aTanzini, Alessandro uhttp://hdl.handle.net/1963/285201262nas a2200121 4500008004300000245007100043210006800114260002800182520085700210100002101067700001601088856003601104 2008 en_Ud 00aOn semistable principal bundles over a complex projective manifold0 asemistable principal bundles over a complex projective manifold bOxford University Press3 aLet G be a simple linear algebraic group defined over the complex numbers. Fix a proper parabolic subgroup P of G and a nontrivial antidominant character \\\\chi of P. We prove that a holomorphic principal G-bundle E over a connected complex projective manifold M is semistable and the second Chern class of its adjoint bundle vanishes in rational cohomology if and only if the line bundle over E/P defined by \\\\chi is numerically effective. Similar results remain valid for principal bundles with a reductive linear algebraic group as the structure group. These generalize an earlier work of Y. Miyaoka where he gave a characterization of semistable vector bundles over a smooth projective curve. Using these characterizations one can also produce similar criteria for the semistability of parabolic principal bundles over a compact Riemann surface.1 aBiswas, Indranil1 aBruzzo, Ugo uhttp://hdl.handle.net/1963/341801055nas a2200109 4500008004300000245006600043210006600109520069300175100001600868700002500884856003600909 2007 en_Ud 00aMetrics on semistable and numerically effective Higgs bundles0 aMetrics on semistable and numerically effective Higgs bundles3 aWe consider fibre metrics on Higgs vector bundles on compact K\\\\\\\"ahler manifolds, providing notions of numerical effectiveness and numerical flatness in terms of such metrics. We prove several properties of bundles satisfying such conditions and in particular we show that numerically flat Higgs bundles have vanishing Chern classes, and that they admit filtrations whose quotients are stable flat Higgs bundles. We compare these definitions with those previously given in the case of projective varieties. Finally we study the relations between numerically effectiveness and semistability, providing semistability criteria for Higgs bundles on projective manifolds of any dimension.1 aBruzzo, Ugo1 aGrana-Otero, Beatriz uhttp://hdl.handle.net/1963/184000810nas a2200109 4500008004300000245004200043210004200085520049600127100001600623700002500639856003600664 2007 en_Ud 00aNumerically flat Higgs vector bundles0 aNumerically flat Higgs vector bundles3 aAfter providing a suitable definition of numerical effectiveness for Higgs bundles, and a related notion of numerical flatness, in this paper we prove, together with some side results, that all Chern classes of a Higgs-numerically flat Higgs bundle vanish, and that a Higgs bundle is Higgs-numerically flat if and only if it is has a filtration whose quotients are flat stable Higgs bundles. We also study the relation between these numerical properties of Higgs bundles and (semi)stability.1 aBruzzo, Ugo1 aGrana-Otero, Beatriz uhttp://hdl.handle.net/1963/175700296nas a2200097 4500008004300000245003900043210003900082100001600121700002500137856003600162 2007 en_Ud 00aSemistable principal Higgs bundles0 aSemistable principal Higgs bundles1 aBruzzo, Ugo1 aGrana-Otero, Beatriz uhttp://hdl.handle.net/1963/253300736nas a2200109 4500008004300000245007600043210006900119520036700188100001600555700001900571856003600590 2006 en_Ud 00aNormal bundles to Laufer rational curves in local Calabi-Yau threefolds0 aNormal bundles to Laufer rational curves in local CalabiYau thre3 aWe prove a conjecture by F. Ferrari. Let X be the total space of a nonlinear deformation of a rank 2 holomorphic vector bundle on a smooth rational curve, such that X has trivial canonical bundle and has sections. Then the normal bundle to such sections is computed in terms of the rank of the Hessian of a suitably defined superpotential at its critical points.1 aBruzzo, Ugo1 aRicco, Antonio uhttp://hdl.handle.net/1963/178501043nas a2200109 4500008004300000245005700043210005400100520069600154100001600850700003100866856003600897 2006 en_Ud 00aSemistability vs. nefness for (Higgs) vector bundles0 aSemistability vs nefness for Higgs vector bundles3 aAccording to Miyaoka, a vector bundle E on a smooth projective curve is semistable if and only if a certain numerical class in the projectivized bundle PE is nef. We establish a similar criterion for the semistability of Higgs bundles: namely, such a bundle is semistable if and only if for every integer s between 0 and the rank of E, a suitable numerical class in the scheme parametrizing the rank s locally-free Higgs quotients of E is nef. We also extend this result to higher-dimensional complex projective varieties by showing that the nefness of the above mentioned classes is equivalent to the semistability of the Higgs bundle E together with the vanishing of the discriminant of E.1 aBruzzo, Ugo1 aHernandez Ruiperez, Daniel uhttp://hdl.handle.net/1963/223700859nas a2200121 4500008004300000245007000043210006900113260001300182520046800195100001600663700002200679856003600701 2004 en_Ud 00aSuperlocalization formulas and supersymmetric Yang-Mills theories0 aSuperlocalization formulas and supersymmetric YangMills theories bElsevier3 aBy using supermanifold techniques we prove a generalization of the localization formula in equivariant cohomology which is suitable for studying supersymmetric Yang-Mills theories in terms of ADHM data. With these techniques one can compute the reduced partition functions of topological super Yang-Mills theory with 4, 8 or 16 supercharges. More generally, the superlocalization formula can be applied to any topological field theory in any number of dimensions.1 aBruzzo, Ugo1 aFucito, Francesco uhttp://hdl.handle.net/1963/288600423nas a2200133 4500008004100000245005600041210005500097260001800152100001600170700002100186700002200207700002400229856003600253 2003 en d00aMulti-instanton calculus and equivariant cohomology0 aMultiinstanton calculus and equivariant cohomology bSISSA Library1 aBruzzo, Ugo1 aMorales, Jose F.1 aFucito, Francesco1 aTanzini, Alessandro uhttp://hdl.handle.net/1963/164500851nas a2200145 4500008004300000245005500043210005500098260001000153520041100163100002200574700001600596700003100612700002600643856003600669 2002 en_Ud 00aRelatively stable bundles over elliptic fibrations0 aRelatively stable bundles over elliptic fibrations bWiley3 aWe consider a relative Fourier-Mukai transform defined on elliptic fibrations over an arbitrary normal base scheme. This is used to construct relative Atiyah sheaves and generalize Atiyah\\\'s and Tu\\\'s results about semistable sheaves over elliptic curves to the case of elliptic fibrations. Moreover we show that this transform preserves relative (semi)stability of sheaves of positive relative degree.1 aBartocci, Claudio1 aBruzzo, Ugo1 aHernandez Ruiperez, Daniel1 aMunoz Porras, Jose M. uhttp://hdl.handle.net/1963/313200661nas a2200121 4500008004300000245006900043210006900112260001300181520027600194100001600470700001700486856003600503 2001 en_Ud 00aComplex Lagrangian embeddings of moduli spaces of vector bundles0 aComplex Lagrangian embeddings of moduli spaces of vector bundles bElsevier3 aBy means of a Fourier-Mukai transform we embed moduli spaces of stable bundles on an algebraic curve C as isotropic subvarieties of moduli spaces of mu-stable bundles on the Jacobian variety J(C). When g(C)=2 this provides new examples of special Lagrangian submanifolds.1 aBruzzo, Ugo1 aPioli, Fabio uhttp://hdl.handle.net/1963/288500426nas a2200121 4500008004100000245008500041210006900126260001800195100001600213700002200229700001700251856003600268 2001 en d00aA Fourier transform for sheaves on real tori. I. The equivalence Sky(T)~ Loc (T)0 aFourier transform for sheaves on real tori I The equivalence Sky bSISSA Library1 aBruzzo, Ugo1 aMarelli, Giovanni1 aPioli, Fabio uhttp://hdl.handle.net/1963/152600437nas a2200133 4500008004100000245006500041210005600106260001800162100001600180700002200196700002400218700002500242856003600267 2001 en d00aOn the Multi-Instanton Measure for Super Yang-Mills Theories0 aMultiInstanton Measure for Super YangMills Theories bSISSA Library1 aBruzzo, Ugo1 aFucito, Francesco1 aTanzini, Alessandro1 aTravaglini, Gabriele uhttp://hdl.handle.net/1963/153100735nas a2200133 4500008004300000245004700043210004700090260001300137520035400150100002200504700001600526700002300542856003600565 1999 en_Ud 00aCategorial mirror symmetry for K3 surfaces0 aCategorial mirror symmetry for K3 surfaces bSpringer3 aWe study the structure of a modified Fukaya category ${\\\\frak F}(X)$ associated with a K3 surface $X$, and prove that whenever $X$ is an elliptic K3 surface with a section, the derived category of $\\\\fF(X)$ is equivalent to a subcategory of the derived category ${\\\\bold D}(\\\\hat X)$ of coherent sheaves on the mirror K3 surface $\\\\hat X$.1 aBartocci, Claudio1 aBruzzo, Ugo1 aSanguinetti, Guido uhttp://hdl.handle.net/1963/288700706nas a2200121 4500008004300000245006300043210006200106260001300168520032800181100001600509700002300525856003600548 1998 en_Ud 00aMirror Symmetry on K3 Surfaces as a Hyper-Kähler Rotation0 aMirror Symmetry on K3 Surfaces as a HyperKähler Rotation bSpringer3 aWe show that under the hypotheses of Strominger, Yau and Zaslow\\\'s paper, a mirror partner of a K3 surface $X$ with a fibration in special Lagrangian tori can be obtained by rotating the complex structure of $X$ within its hyperk\\\\\\\"ahler family of complex structures. The same hypotheses force the B-field to vanish.1 aBruzzo, Ugo1 aSanguinetti, Guido uhttp://hdl.handle.net/1963/288800757nas a2200121 4500008004100000245007900041210006900120260001800189520035600207100001600563700002100579856003500600 1994 en d00aHilbert schemes of points on some K3 surfaces and Gieseker stable boundles0 aHilbert schemes of points on some K3 surfaces and Gieseker stabl bSISSA Library3 aBy using a Fourier-Mukai transform for sheaves on K3 surfaces we show that for a wide class of K3 surfaces $X$ the punctual Hilbert schemes $\\\\Hilb^n(X)$ can be identified, for all $n\\\\geq 1$, with moduli spaces of Gieseker stable vector bundles on $X$ of rank $1+2n$. We also introduce a new Fourier-Mukai type transform for such surfaces.

1 aBruzzo, Ugo1 aMaciocia, Antony uhttp://hdl.handle.net/1963/93700655nas a2200133 4500008004100000245005500041210005400096260001800150520026000168100002000428700002200448700001600470856003500486 1990 en d00aChern-Simons forms on principal superfiber bundles0 aChernSimons forms on principal superfiber bundles bSISSA Library3 aA graded Weil homomorphism is defined for principal superfiber bundles and the related transgression (or Chern-Simons) forms are introduced. As an example of the application of these concepts, a ``superextension\\\'\\\' of the Dirac monopole is discussed.1 aLandi, Giovanni1 aBartocci, Claudio1 aBruzzo, Ugo uhttp://hdl.handle.net/1963/590