A Special Case of the Buchsbaum-eisenbud-horrocks Rank Conjecture
نویسنده
چکیده
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-Söderberg 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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