Counting Hyperelliptic curves on Abelian surfaces with Quasi-modular forms

2012/02/09 by Rose, Simon
#14K99 #14N10 #14N35 #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1202.2094

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.

Related

• Curve counting on abelian surfaces and threefolds
• On hyperelliptic modular curves over function fields
• Generating functions for the number of curves on Abelian surfaces
• MacMahon's sum-of-divisors functions, Chebyshev polynomials, and Quasi-modular forms
• Counting hyperelliptic curves