Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: G-bundles on Abelian surfaces, hyperkahler manifolds, and stringy Hodge
  numbers   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.

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The categories of this paper are: mtrl-th
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The categories of this paper are: funct-an
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The categories of this paper are: acc-phys
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The categories of this paper are: math-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: nlin
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The categories of this paper are: chao-dyn
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The categories of this paper are: bayes-an
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The categories of this paper are: comp-gas
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The categories of this paper are: solv-int
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The categories of this paper are: q-bio
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The categories of this paper are: quant-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: atom-ph
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The categories of this paper are: q-fin