2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/135350We 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.This paper contains an appendix by Georg Hein: Semistability of the general syzygy bundle. The new version is quite newAlgebraic GeometryCommutative Algebra13A35; 13D02; 14D20; 14H60; 14J60text