Regularity stabilization for the powers of graded m-primary ideals

2013/10/17 by Chardin, Marc
#13A30 #13D02 #13D45 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1310.4727

Abstract

This Note provides first a generalization of the stabilization result of Eisenbud and Ulrich for the regularity of powers of a m-primary ideal to the case of ideals that are not generated in a single degree. We then partially extend our previous results expressing this stabilization degree in term of the regularity of a specific graded strand of the Rees ring : The natural extension of the statement holds at least if the stabilization index or the regularity is greater than the number of variables. In any case a precise comparison is given.

Related

• Stabilization of the Regularity of Powers of An Ideal
• Regularity defect stabilization of powers of an ideal
• Castelnuovo-Mumford regularity and powers
• The strong Rees property of powers of the maximal ideal and Takahashi-Dao's question
• Comparison of stability indices of powers of graded ideals