G-bundles on Abelian surfaces, hyperk\"aler manifolds, and stringy Hodge numbers

Jim Bryan; Ron Donagi; Naichung Conan Leung

Makale detayları

G-bundles on Abelian surfaces, hyperk\"aler manifolds, and stringy Hodge numbers

Yazarlar:

Jim Bryan | Ron Donagi | Naichung Conan Leung

Yayıncı:

TUBITAK

Ana Başlıklar:

Matematik

Dergi:

Turkish Journal of Mathematics 2001 Vol.25 Issue 1, pp.195-236

Belge Tipi:

Makale

Yayın Tarihi:

12/2000

Belge Dili:

İngilizce

Document ID (Org No.):

2000749137

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098

Özet:

 

We study the moduli space MG (A) of flat G-bundles on an Abelian  surface A, where G is a compact, simple, simply connected, connected  Lie group. Equivalently, MG (A) is the (coarse) moduli space of  s-equivalence classes of holomorphic semi-stable G\cnums -bundles  with trivial Chern classes.    MG (A) has the structure of a hyperk\"ahler orbifold. We show that  when G is Sp(n) or SU (n), MG (A) has a natural hyperk\"ahler  desingularization which we exhibit as a moduli space of G\cnums  -bundles with an altered stability condition. In this way, we obtain the  two known families of hyperk\"ahler 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 MG (A) does  \emph{not} admit a hyperk\"ahler resolution.    \sloppy{Inspired by the physicists Vafa and Zaslow, Batyrev and Dais define  stringy Hodge numbers'' for certain orbifolds. These numbers have been  proven to agree with the Hodge numbers of a crepant resolution (when it  exists). We directly compute the stringy Hodge numbers of MSU (n) (A)  and MSp (n) (A), thus deriving formulas (originally due to G\"ottsche  and G\"ottsche-Soergel) for the Hodge numbers of the Hilbert schemes of  points on K3 surfaces and generalized Kummer varieties.}.

Makale detayları

G-bundles on Abelian surfaces, hyperk\"aler manifolds, and stringy Hodge numbers

Yazarlar: Jim Bryan | Ron Donagi | Naichung Conan Leung

Yayıncı: TUBITAK

Ana Başlıklar: Matematik

Dergi: Turkish Journal of Mathematics 2001 Vol.25 Issue 1, pp.195-236

Belge Tipi: Makale

Yayın Tarihi: 12/2000

Belge Dili: İngilizce

Document ID (Org No.): 2000749137

Sıklık: İki Aylık

eISSN: 1303-6149

pISSN: 1300-0098

Sayı

Yazarlar:

Jim Bryan | Ron Donagi | Naichung Conan Leung

Yayıncı:

TUBITAK

Ana Başlıklar:

Matematik

Dergi:

Turkish Journal of Mathematics 2001 Vol.25 Issue 1, pp.195-236

Belge Tipi:

Makale

Yayın Tarihi:

12/2000

Belge Dili:

İngilizce

Document ID (Org No.):

2000749137

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098