Looking out for stable syzygy bundles

Autor(en): Brenner, Holger 
Stichwörter: FAMILIES; generic forms; Mathematics; monomial ideals; RESTRICTION; semistable vector bundles; SHEAVES; syzygies; TIGHT CLOSURE; VECTOR-BUNDLES
Erscheinungsdatum: 2008
Herausgeber: ACADEMIC PRESS INC ELSEVIER SCIENCE
Journal: ADVANCES IN MATHEMATICS
Volumen: 219
Ausgabe: 2
Startseite: 401
Seitenende: 427
Zusammenfassung: 
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.
ISSN: 00018708
DOI: 10.1016/j.aim.2008.04.009

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