English

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.

Keywords

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

R2 v1 2026-07-22T16:59:50.378Z