Regularity bounds for Koszul cycles

2012/03/08 by Conca, Aldo, Murai, Satoshi
#13D02 #13D03 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1203.1783

Abstract

We study the module of Koszul cycles Z_t(I,M) of a homogeneous ideal I in a polynomial ring S with respect to a graded module M. Under mild assumptions on the base field we prove that the regularity of Z_t(I,S) is a subadditive function of the homological position t when I is 0-dimensional. For Borel-fixed ideals I and J we prove that the regularity of Z_t(I,S/J) is bounded above by t(1+\reg I)+\reg S/J.

Related

• Regularity of Koszul modules
• Koszul cycles
• Castelnuovo-Mumford regularity of Koszul cycles and Koszul homologies
• Linearity Defect and Regularity over a Koszul Algebra
• Modules of infinite regularity over commutative graded rings