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Looking out for stable syzygy bundles

Holger Brenner
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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.

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Holger Brenner. 2007-08-01. Looking out for stable syzygy bundles. https://arxiv.org/abs/math/0311333

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