Looking out for stable syzygy bundles

• Autores: Holger Brenner
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 219, Nº 2, 2008, págs. 401-427
• Idioma: inglés
• DOI: 10.1016/j.aim.2008.04.009
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• Resumen

  • We study (slope-)stability properties of syzygy bundles on a projective space 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.