Castelnuovo theory and the geometric Schottky problem
Algebraic Geometry
2007-06-26 v4
Abstract
We prove and conjecture results which show that Castelnuovo theory in projective space has a close analogue for abelian varieties. This is related to the geometric Schottky problem: our main result is that a principally polarized abelian variety satisfies a precise version of the Castelnuovo Lemma if and only if it is a Jacobian. This result has a surprising connection to the Trisecant Conjecture. We also give a genus bound for curves in abelian varieties.
Cite
@article{arxiv.math/0407370,
title = {Castelnuovo theory and the geometric Schottky problem},
author = {Giuseppe Pareschi and Mihnea Popa},
journal= {arXiv preprint arXiv:math/0407370},
year = {2007}
}
Comments
17 pages; final version, to appear in J. Reine Angew. Math.; no significant changes, only some small corrections and additions with respect to the previous version