G-bundles on Abelian surfaces, hyperkahler manifolds, and stringy Hodge numbers
| dc.creator | Bryan, Jim | |
| dc.creator | Donagi, Ron | |
| dc.creator | Leung, Naichung Conan | |
| dc.date | 2000-04-25 | |
| dc.date.accessioned | 2026-07-07T04:34:52Z | |
| dc.date.available | 2026-07-07T04:34:52Z | |
| dc.description | We study the moduli space M(G,A) of flat G-bundles on an Abelian surface A, where G is a compact, simple, simply connected, connected Lie group. Equivalently, M(G,A) is the (coarse) moduli space of s-equivalence classes of holomorphic semi-stable G_C-bundles with trivial Chern classes where G_C is the complexified group. M(G,A) has the structure of a hyperkahler orbifold. We show that when G is Sp(n) or SU(n), M(G,A) has a natural hyperkahler desingularization which we exhibit as a moduli space of G_C-bundles with an altered stability condition. In this way, we obtain the two known families of hyperkahler manifolds, the Hilbert scheme of points on a K3 surface and the generalized Kummer varieties. We show that for G not Sp(n) or SU(n), the moduli space M(G,A) does not admit a hyperkahler resolution, in fact, it does not have a crepant resolution. Inspired by the physicists Vafa and Zaslow, Batyrev and Dais define ``stringy Hodge numbers'' for certain orbifolds. These numbers are conjectured to agree with the Hodge numbers of a crepant resolution (when it exists). We compute the stringy Hodge numbers of M(SU(n),A) and M(Sp(n),A) and verify the conjecture in these cases. | |
| dc.description | 37 pages | |
| dc.identifier | https://arxiv.org/abs/math/0004159 | |
| dc.identifier | http://arxiv.org/abs/math/0004159 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/59073 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Differential Geometry | |
| dc.subject | 14D20;14D21;53C26 | |
| dc.title | G-bundles on Abelian surfaces, hyperkahler manifolds, and stringy Hodge numbers | |
| dc.type | text |