Curves of genus g on an abelian variety of dimension g
Herbert Lange, Edoardo Sernesi
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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