1990•Transactions of the American Mathematical SocietyRequires access

Dualizing complexes of affine semigroup rings

Uwe Schäfer, Peter Schenzel

Abstract

For an affine semigroup ring we construct the dualizing complex in terms of the semigroup and the homology of the face lattice of the polyhedral cone spanned by the semigroup. As a consequence there are characterizations of locally Cohen-Macaulay rings, Buchsbaum rings, and Cohen-Macaulay rings as well as Serre’s condition S l {\mathcal {S}_l} .

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Key concepts: Semigroup, Mathematics, Affine transformation, Algorithm, Pure mathematics