1996/02/28 by Chikashi Miyazaki, Miyazaki, Chikashi, Wolfgang Vogel +1
Mathematics · #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #alg-geom #math.AG
paper · pdf · doi:10.48550/arxiv.alg-geom/9602021
LaTeX, 18 pages
arxiv created 1996/02/28 · arxiv updated 2015/06/30
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 ≥ 0 the minimal generators of the p-th syzygy module of the defining ideal I of X occur in degree ≤ 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.