Curves of genus g on an abelian variety of dimension g

2002/06/24 by Herbert Lange, Lange, Herbert, Edoardo Sernesi +1
Mathematics · #14K05 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14K05

paper · pdf · doi:10.48550/arxiv.math/0206247

12 pages

arxiv created 2002/06/24 · arxiv updated 2009/11/30

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.

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