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 is a finitely generated graded module over a standard graded algebra and is an ideal of , it is known from work of Cutkosky, Herzog, Kodiyalam, Römer, Trung and Wang that the Castelnuovo-Mumford regularity of has the form when . We give an explicit bound on the for which this is true, under the hypotheses that is generated in a single degree and 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

Email:
eisenbud@math.berkeley.edu

**Bernd Ulrich**

Affiliation:
Department of Mathematics, Purdue University, West Lafayette, Indiana 47907

Email:
ulrich@math.purdue.edu

DOI:
https://doi.org/10.1090/S0002-9939-2011-11270-X

Received by editor(s):
January 3, 2011

Published electronically:
October 18, 2011

Communicated by:
Harm Derksen

Article copyright:
© Copyright 2011
American Mathematical Society