Curves of genus g on an abelian variety of dimension g

Details Curves of genus g on an abelian variety of dimension g Curves of genus g on an abelian variety of dimension g

2002-06-24

arxiv.org/abs/math/0206247v1

Mathematics

Algebraic Geometry

12 pages

Scientific paper

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.

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