Looking out for stable syzygy bundles

By Holger Brenner. 2003

52 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/ec4e418b471bdad883715dd68c617f7bc5885405

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In Algebra and Number Theory

In Computational Theory and Mathematics

In Geometry and Topology

Citations in the corpus

Syzygy Bundles on P^2 and the Weak Lefschetz Property (2006, methodology): “These are c(1,2) = a(1,2,0) + a(0,2,1)u + 2a(0,1,2)uv + a(1,1,1)v + a(1,0,2)v 2 + 3a(0,0,3)uv 2 and c(2,1) = a(2,1,0) + a(0,1,2)u 2 + a(2,0,1)v + a(1,1,1)u + 2a(1,0,2)uv + 3a(0,0,3)u (2)v.”
Monomial ideals, almost complete intersections and the Weak Lefschetz property (2008, background): “This class of ideals was first considered in [3], Corollary 7.”