%0 Report
%D 2017
%T Semistable Higgs Bundles on Calabi-Yau Manifolds
%A Ugo Bruzzo
%A Valeriano Lanza
%A Alessio Lo Giudice
%X 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.
%G en
%U http://preprints.sissa.it/handle/1963/35295
%1 35601
%2 Mathematics
%4 1
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%0 Thesis
%D 2013
%T Some topics on Higgs bundles over projective varieties and their moduli spaces
%A Alessio Lo Giudice
%K Algebraic Geometry, Moduli spaces, Vector bundles
%X In this thesis we study vector bundles on projective varieties and their moduli spaces. In Chapters 2, 3 and 4 we recall some basic notions as Higgs bundles, decorated bundles and generalized parabolic sheaves and introduce the problem we want to study. In chapter 5, we study Higgs bundles on nodal curves. After moving the problem on the normalization of the curve, starting from a Higgs bundle we obtain a generalized parabolic Higgs bundle. Using decorated bundles we are able to construct a projective moduli space which parametrizes equivalence classes of Higgs bundles on a nodal curve X. This chapter is an extract of a joint work with Andrea Pustetto Later on Chapter 6 is devoted to the study of holomorphic pairs (or twisted Higgs bundles) on elliptic curve. Holomorphic pairs were introduced by Nitsure and they are a natural generalization of the concept of Higgs bundles. In this Chapter we extend a result of E. Franco, O. Garc\'ia-Prada And P.E. Newstead valid for Higgs bundles to holomorphic pairs. Finally the last Chapter describes a joint work with Professor Ugo Bruzzo. We study Higgs bundles over varieties with nef tangent bundle. In particular generalizing a result of Nitsure we prove that if a Higgs bundle $(E,\phi)$ over the variety X with nef tangent remains semisatble when pulled-back to any smooth curve then it discrimiant vanishes.
%I SISSA
%G en
%1 7134
%2 Mathematics
%4 1
%# MAT/03 GEOMETRIA
%$ Submitted by Alessio Lo Giudice (logiudic@sissa.it) on 2013-09-25T11:22:08Z
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%0 Journal Article
%J Le Matematiche (Catania), volume 66, Issue no.2, (2011), pages : 153-187
%D 2011
%T Cones of divisors of blow-ups of projective spaces
%A Alessio Lo Giudice
%A Salvatore Cacciola
%A M. Donten-Bury
%A O. Dumitrescu
%A J. Park
%K Mori dream space
%X We investigate Mori dream spaces obtained by blowing-up the n-dimensional complex projective space at n+1, n+2 or n+3 points in very general position. Using toric techniques we study the movable cone of the blow-up of Pn at n+1 points, its decomposition into nef chambers and the action of theWeyl group on the set of chambers. Moreover, using different methods, we explicitly write down the equations of the movable cone also for Pn blown-up at n+2 points.
%B Le Matematiche (Catania), volume 66, Issue no.2, (2011), pages : 153-187
%I Università degli Studi di Catania. Dipartimento di matematica
%G en
%U http://hdl.handle.net/1963/6613
%1 6462
%2 Mathematics
%4 1
%# MAT/03 GEOMETRIA
%$ Submitted by Alessio Lo Giudice (logiudic@sissa.it) on 2013-03-01T08:45:50Z
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%R 10.4418/2011.66.2.13