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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Notes on regularity stabilization
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by David Eisenbud and Bernd Ulrich PDF
Proc. Amer. Math. Soc. 140 (2012), 1221-1232 Request permission


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:
  • Bernd Ulrich
  • Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
  • MR Author ID: 175910
  • Email:
  • Received by editor(s): January 3, 2011
  • Published electronically: October 18, 2011
  • Communicated by: Harm Derksen
  • © Copyright 2011 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 140 (2012), 1221-1232
  • MSC (2010): Primary 13D02, 13C99, 13P20, 14N05
  • DOI:
  • MathSciNet review: 2869107