Infinitesimal Castelnuovo Theory in Abelian Varieties
Algebraic Geometry
2021-01-28 v2
Abstract
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.
Keywords
Cite
@article{arxiv.0706.2239,
title = {Infinitesimal Castelnuovo Theory in Abelian Varieties},
author = {Marti Lahoz},
journal= {arXiv preprint arXiv:0706.2239},
year = {2021}
}
Comments
The proofs and the results were corrected and improved in arXiv:1410.4813