Bounds on cohomology and Castelnuovo-Mumford regularity

Details Bounds on cohomology and Castelnuovo-Mumford regularity Bounds on cohomology and Castelnuovo-Mumford regularity

1996-02-28

arxiv.org/abs/alg-geom/9602021v1

Mathematics

Algebraic Geometry

LaTeX, 18 pages

Scientific paper

The Castelnuovo-Mumford regularity reg(X) of a projective scheme X was introduced by Mumford by generalizing ideas of Castelnuovo. The interest in this concept stems partly from the fact that X is m-regular if and only if for every p \geq 0 the minimal generators of the p-th syzygy module of the defining ideal I of X occur in degree \leq m + p. There are some bounds in the case that X is a locally Cohen-Macaulay scheme. The aim of this paper is to extend and improve these results for so-called (k,r)-Buchsbaum schemes. In order to prove our theorems, we need to apply a spectral sequence. We conclude by describing two sharp examples and open problems.

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