Notes on regularity stabilization
Authors:
David Eisenbud and Bernd Ulrich
Journal:
Proc. Amer. Math. Soc. 140 (2012), 1221-1232
MSC (2010):
Primary 13D02, 13C99, 13P20, 14N05
DOI:
https://doi.org/10.1090/S0002-9939-2011-11270-X
Published electronically:
October 18, 2011
MathSciNet review:
2869107
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Abstract | References | Similar Articles | Additional Information
Abstract: When $M$ is a finitely generated graded module over a standard graded algebra $S$ and $I$ is an ideal of $S$, it is known from work of Cutkosky, Herzog, Kodiyalam, Römer, Trung and Wang that the Castelnuovo-Mumford regularity of $I^mM$ has the form $dm+e$ when $m\gg 0$. We give an explicit bound on the $m$ for which this is true, under the hypotheses that $I$ is generated in a single degree and $M/IM$ has finite length, and we explore the phenomena that occur when these hypotheses are not satisfied. Finally, we prove a regularity bound for a reduced, equidimensional projective scheme of codimension 2 that is similar to the bound in the Eisenbud-Goto conjecture, under the additional hypotheses that the scheme lies on a quadric and has nice singularities.
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Additional Information
David Eisenbud
Affiliation:
Department of Mathematics, University of California, Berkeley, Berkeley, California 94720
MR Author ID:
62330
ORCID:
0000-0002-5418-5579
Email:
eisenbud@math.berkeley.edu
Bernd Ulrich
Affiliation:
Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
MR Author ID:
175910
Email:
ulrich@math.purdue.edu
Received by editor(s):
January 3, 2011
Published electronically:
October 18, 2011
Communicated by:
Harm Derksen
Article copyright:
© Copyright 2011
American Mathematical Society