Infinitesimal Castelnuovo Theory in Abelian Varieties

Details Infinitesimal Castelnuovo Theory in Abelian Varieties Infinitesimal Castelnuovo Theory in Abelian Varieties

2007-06-15

arxiv.org/abs/0706.2239v1

Mathematics

Algebraic Geometry

15 pages. Any commentaries are welcomed

Scientific paper

The purpose of this article is to show that the Castelnuovo theory for abelian varieties, developed by G. Pareschi and M. Popa, can be infinitesimalized. More precisely, we prove that an irreducible principally polarized abelian variety has a finite scheme in extremal position, in the sense of Castelnuovo theory for abelian varieties, if, and only if, it is a Jacobian and the scheme is contained in a unique Abel-Jacobi curve.

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