Curves of genus g on an abelian variety of dimension g

Abstract

In this paper we prove a general theorem concerning the number of translation classes of curves of genus $g$ belonging to a fixed cohomology class in a polarized abelian variety of dimension $g$. For $g=2$ we recover results of Göttsche and Bryan-Leung. For $g=3$ we deduce explicit numbers for these classes.

12 pages