Looking out for stable syzygy bundles
Algebraic Geometry
2007-08-01 v3 Commutative Algebra
Abstract
We study (slope-)stability properties of syzygy bundles on a projective space P^N given by ideal generators of a homogeneous primary ideal. In particular we give a combinatorial criterion for a monomial ideal to have a semistable syzygy bundle. Restriction theorems for semistable bundles yield the same stability results on the generic complete intersection curve. From this we deduce a numerical formula for the tight closure of an ideal generated by monomials or by generic homogeneous elements in a generic two-dimensional complete intersection ring.
Cite
@article{arxiv.math/0311333,
title = {Looking out for stable syzygy bundles},
author = {Holger Brenner},
journal= {arXiv preprint arXiv:math/0311333},
year = {2007}
}
Comments
This paper contains an appendix by Georg Hein: Semistability of the general syzygy bundle. The new version is quite new