Multiplicities of Semidualizing Modules

Abstract

A finitely generated module C over a commutative noetherian ring R is semidualizing if Hom R(C, C) ≅ R and for all i ≥ 1. For certain local Cohen–Macaulay rings (R, 𝔪), we verify the equality of Hilbert-Samuel multiplicities eR(J; C) = eR(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.