Looking out for stable syzygy bundles

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. (C) 2008 Elsevier Inc. All rights reserved.