A special case of the Buchsbaum-Eisenbud-Horrocks rank conjecture

Details A special case of the Buchsbaum-Eisenbud-Horrocks rank conjecture A special case of the Buchsbaum-Eisenbud-Horrocks rank conjecture

2009-02-02

arxiv.org/abs/0902.0316v2

Mathematics

Commutative Algebra

11 pages, 1 figure

Scientific paper

The Buchsbaum-Eisenbud-Horrocks rank conjecture proposes lower bounds for the Betti numbers of a graded module M based on the codimension of M. We prove a special case of this conjecture via Boij-Soederberg theory. More specifically, we show that the conjecture holds for graded modules where the regularity of M is small relative to the minimal degree of a first syzygy of M. Our approach also yields an asymptotic lower bound for the Betti numbers of powers of an ideal generated in a single degree.

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