TY - RPRT
T1 - Semistable Higgs Bundles on Calabi-Yau Manifolds
Y1 - 2017
A1 - Ugo Bruzzo
A1 - Valeriano Lanza
A1 - Alessio Lo Giudice
AB - We 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.
UR - http://preprints.sissa.it/handle/1963/35295
U1 - 35601
U2 - Mathematics
U4 - 1
ER -
TY - RPRT
T1 - Symplectic instanton bundles on P3 and 't Hooft instantons
Y1 - 2013
A1 - Ugo Bruzzo
A1 - Dimitri Markushevich
A1 - Alexander Tikhomirov
AB - We 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.
PB - arXiv:1312.5554 [math.AG]
UR - http://urania.sissa.it/xmlui/handle/1963/34486
N1 - This preprint has been published with the title "Moduli of symplectic instanton vector bundles of higher rank on projective space P-3 " in CENTRAL EUROPEAN JOURNAL OF MATHEMATICS, Volume: 10, issue 4, Augst 2012, pages 1232-1245.
U1 - 34675
U2 - Mathematics
U4 - 1
U5 - MAT/03
ER -
TY - JOUR
T1 - Semistable and numerically effective principal (Higgs) bundles
JF - Advances in Mathematics 226 (2011) 3655-3676
Y1 - 2011
A1 - Ugo Bruzzo
A1 - Beatriz Grana-Otero
AB - We 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.
PB - Elsevier
UR - http://hdl.handle.net/1963/3638
U1 - 666
U2 - Mathematics
U3 - Mathematical Physics
ER -
TY - JOUR
T1 - On semistable principal bundles over complex projective manifolds, II
JF - Geom. Dedicata 146 (2010) 27-41
Y1 - 2010
A1 - Indranil Biswas
A1 - Ugo Bruzzo
AB - Let (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.
UR - http://hdl.handle.net/1963/3404
U1 - 928
U2 - Mathematics
U3 - Mathematical Physics
ER -
TY - JOUR
T1 - On semistable principal bundles over a complex projective manifold
JF - Int. Math. Res. Not. vol. 2008, article ID rnn035
Y1 - 2008
A1 - Indranil Biswas
A1 - Ugo Bruzzo
AB - Let 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.
PB - Oxford University Press
UR - http://hdl.handle.net/1963/3418
U1 - 917
U2 - Mathematics
U3 - Mathematical Physics
ER -
TY - RPRT
T1 - Semistable principal Higgs bundles
Y1 - 2007
A1 - Ugo Bruzzo
A1 - Beatriz Grana-Otero
UR - http://hdl.handle.net/1963/2533
U1 - 1585
U2 - Mathematics
U3 - Mathematical Physics
ER -
TY - JOUR
T1 - Semistability vs. nefness for (Higgs) vector bundles
JF - Differential Geom. Appl. 24 (2006) 403-416
Y1 - 2006
A1 - Ugo Bruzzo
A1 - Daniel Hernandez Ruiperez
AB - According 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.
UR - http://hdl.handle.net/1963/2237
U1 - 2007
U2 - Mathematics
U3 - Mathematical Physics
ER -
TY - JOUR
T1 - Superlocalization formulas and supersymmetric Yang-Mills theories
JF - Nucl. Phys. B 678 (2004) 638-655
Y1 - 2004
A1 - Ugo Bruzzo
A1 - Francesco Fucito
AB - By 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.
PB - Elsevier
UR - http://hdl.handle.net/1963/2886
U1 - 1814
U2 - Mathematics
U3 - Mathematical Physics
ER -