Communications in Number Theory and Physics

Volume 8 (2014)

Number 2

Counting hyperelliptic curves on an Abelian surface with quasi-modular forms

Pages: 243 – 293

DOI: http://dx.doi.org/10.4310/CNTP.2014.v8.n2.a2

Author

Simon C. F. Rose (Department of Math and Statistics, Queen’s University. Kingston, Ontario, Canada; and Fields Institute, University of Toronto, Ontario, Canada)

Abstract

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.

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