Multiplicities of semidualizing modules
Commutative Algebra
2012-09-04 v2
Abstract
A finitely generated module C over a commutative noetherian ring R is semidualizing if Hom_R(C,C) \cong R and Ext^i_R(C,C) = 0 for all i \geq 1. For certain local Cohen-Macaulay rings (R,m), we verify the equality of Hilbert-Samuel multiplicities e_R(J;C) = e_R(J;R) for all semidualizing R-modules C and all m-primary ideals J. The classes of rings we investigate include those that are determined by ideals defining fat point schemes in projective space or by monomial ideals.
Cite
@article{arxiv.1001.2632,
title = {Multiplicities of semidualizing modules},
author = {Susan M. Cooper and Sean Sather-Wagstaff},
journal= {arXiv preprint arXiv:1001.2632},
year = {2012}
}
Comments
12 pages, uses xypic; v.2 has material on enumeration removed. to appear in Comm. Algebra