Communications in Number Theory and Physics
Volume 8 (2014)
Counting hyperelliptic curves on an Abelian surface with quasi-modular forms
Pages: 243 – 293
In this paper, we produce a generating function for the number of hyperelliptic curves (up to translation) on a polarized Abelian surface 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.