133 research outputs found
A special case of the Buchsbaum-Eisenbud-Horrocks rank conjecture
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.Comment: 11 pages, 1 figur
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