Curves of genus g on an abelian variety of dimension g
  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 G\"ottsche and Bryan-Leung. For $g = 3$ we deduce explicit numbers for these classes. 
Herbert Lange and Edoardo Sernesi