Stabilization of the Regularity of Powers of An Ideal

2010/12/04 by David Eisenbud, Eisenbud, David, Bernd Ulrich +1 · 1 citation
Mathematics · #13C99 #13D02 #13P20 #14N05 #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1012.0951

openalex publication_date 2010/12/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 >> 0. We give an explicit bound on the mfor 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 [1984], under the additional hypotheses that the scheme lies on a quadric and has nice singularities.

Cited by

• The eventual shape of Betti tables of powers of ideals

Related

• Bounds for the Castelnuovo-Mumford regularity of modules
• Regularity defect stabilization of powers of an ideal
• Castelnuovo-Mumford regularity and powers
• Regularity stabilization for the powers of graded m-primary ideals
• Castelnuovo Mumford Regularity with respect to multigraded ideals