Counting Hyperelliptic curves on Abelian surfaces with Quasi-modular forms

Details Counting Hyperelliptic curves on Abelian surfaces with Quasi-modular forms Counting Hyperelliptic curves on Abelian surfaces with Quasi-modular forms

2012-02-09

arxiv.org/abs/1202.2094v2

Mathematics

Algebraic Geometry

41 pages, 2 figures

Scientific paper

In this paper we produce a generating function for the number of
hyperelliptic curves (up to translation) on a polarized Abelian surfaces using
the crepant resolution conjecture and the Yau-Zaslow formula. We present a
formula to compute these in terms of MacMahon's generalized sum-of-divisors
functions, and prove that they are quasi-modular forms.

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