@article {2017,
title = {Semistable Higgs Bundles on Calabi-Yau Manifolds},
number = {SISSA;40/2017/MATE;},
year = {2017},
abstract = {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.},
url = {http://preprints.sissa.it/handle/1963/35295},
author = {Ugo Bruzzo and Valeriano Lanza and Alessio Lo Giudice}
}
@article {2013,
title = {Symplectic instanton bundles on P3 and {\textquoteright}t Hooft instantons},
year = {2013},
note = {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.},
institution = {arXiv:1312.5554 [math.AG]},
abstract = {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 {\textquoteright}t Hooft instantons.},
url = {http://urania.sissa.it/xmlui/handle/1963/34486},
author = {Ugo Bruzzo and Dimitri Markushevich and Alexander Tikhomirov}
}
@article {2011,
title = {Semistable and numerically effective principal (Higgs) bundles},
journal = {Advances in Mathematics 226 (2011) 3655-3676},
number = {SISSA;27/2009/FM},
year = {2011},
publisher = {Elsevier},
abstract = {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 Hermitian{\textendash}Yang{\textendash}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.},
doi = {10.1016/j.aim.2010.10.026},
url = {http://hdl.handle.net/1963/3638},
author = {Ugo Bruzzo and Beatriz Grana-Otero}
}
@article {2010,
title = {On semistable principal bundles over complex projective manifolds, II},
journal = {Geom. Dedicata 146 (2010) 27-41},
number = {SISSA;85/2008/FM},
year = {2010},
abstract = {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.},
doi = {10.1007/s10711-009-9424-8},
url = {http://hdl.handle.net/1963/3404},
author = {Indranil Biswas and Ugo Bruzzo}
}
@article {2008,
title = {On semistable principal bundles over a complex projective manifold},
journal = {Int. Math. Res. Not. vol. 2008, article ID rnn035},
number = {arXiv.org;0803.4042v1},
year = {2008},
publisher = {Oxford University Press},
abstract = {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.},
doi = {10.1093/imrn/rnn035},
url = {http://hdl.handle.net/1963/3418},
author = {Indranil Biswas and Ugo Bruzzo}
}
@article {2007,
title = {Semistable principal Higgs bundles},
number = {SISSA;89/2007/MP},
year = {2007},
url = {http://hdl.handle.net/1963/2533},
author = {Ugo Bruzzo and Beatriz Grana-Otero}
}
@article {2006,
title = {Semistability vs. nefness for (Higgs) vector bundles},
journal = {Differential Geom. Appl. 24 (2006) 403-416},
number = {arXiv.org;math/0310040v3},
year = {2006},
abstract = {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.},
doi = {10.1016/j.difgeo.2005.12.007},
url = {http://hdl.handle.net/1963/2237},
author = {Ugo Bruzzo and Daniel Hernandez Ruiperez}
}
@article {2004,
title = {Superlocalization formulas and supersymmetric Yang-Mills theories},
journal = {Nucl. Phys. B 678 (2004) 638-655},
number = {arXiv.org;math-ph/0310036v1},
year = {2004},
publisher = {Elsevier},
abstract = {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.},
doi = {10.1016/j.nuclphysb.2003.11.033},
url = {http://hdl.handle.net/1963/2886},
author = {Ugo Bruzzo and Francesco Fucito}
}