Curves of genus g on an abelian variety of dimension g

Lange, Herbert; Sernesi, Edoardo

Curves of genus g on an abelian variety of dimension g

Authors

Description

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