A special case of the Buchsbaum-Eisenbud-Horrocks rank conjecture
Commutative Algebra
2018-04-30 v2 Algebraic Geometry
Abstract
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.
Keywords
Cite
@article{arxiv.0902.0316,
title = {A special case of the Buchsbaum-Eisenbud-Horrocks rank conjecture},
author = {Daniel Erman},
journal= {arXiv preprint arXiv:0902.0316},
year = {2018}
}
Comments
11 pages, 1 figure