00688nas a2200121 4500008004100000245005300041210005200094520031100146100001600457700002100473700002400494856004800518 2017 en d00aSemistable Higgs Bundles on Calabi-Yau Manifolds0 aSemistable Higgs Bundles on CalabiYau Manifolds3 aWe provide a partial classification of semistable Higgs bundles over a simply connected Calabi-Yau manifold. Applications to a conjecture about a special class of semistable Higgs bundles are given. In particular, the conjecture is proved for K3 and Enriques surfaces, and some related classes of surfaces.1 aBruzzo, Ugo1 aLanza, Valeriano1 aLo Giudice, Alessio uhttp://preprints.sissa.it/handle/1963/3529500812nas 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/1963/3448601465nas 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 Hermitianâ€“Yangâ€“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/1963/363801102nas 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/1963/340401262nas 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/1963/341800296nas a2200097 4500008004300000245003900043210003900082100001600121700002500137856003600162 2007 en_Ud 00aSemistable principal Higgs bundles0 aSemistable principal Higgs bundles1 aBruzzo, Ugo1 aGrana-Otero, Beatriz uhttp://hdl.handle.net/1963/253301043nas 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/1963/2886