Algebraic Geometry Seminar: Simon Rose
Topic
Counting Hyperelliptic Curves on Abelian Surfaces with Quasimodular Forms
Speakers
Details
Abstract:
In this talk we will present a formula to count the number of hyperelliptic curves on a polarized Abelian surface, up to translation.
This formula is obtained using orbifold Gromov-Witten theory, the crepant resolution conjection and the Yau-Zaslow formula to related hyperelliptic curves to rational curves on the Kummer surface Km(A). We will show how this formula can be described in terms of certain generating functions studied by P. A. MacMahon, which turn out to be quasimodular forms.
