Counting Hyperelliptic curves on Abelian surfaces with Quasi-modular forms
Algebraic Geometry
2012-04-18 v2 Combinatorics
Abstract
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.
Cite
@article{arxiv.1202.2094,
title = {Counting Hyperelliptic curves on Abelian surfaces with Quasi-modular forms},
author = {Simon Rose},
journal= {arXiv preprint arXiv:1202.2094},
year = {2012}
}
Comments
41 pages, 2 figures