Multiplicities of semidualizing modules
Abstract
A finitely generated module C over a commutative noetherian ring R is semidualizing if HomR(C,C) R and ExtiR(C,C) = 0 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.
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