Counting Hyperelliptic curves on Abelian surfaces with Quasi-modular   forms
  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. 
Simon Rose
math.AG math.CO