Annihilators of graded components of the canonical module, and the core of standard graded algebras

Fouli, Louiza; Polini, Claudia; Ulrich, Bernd

doi:10.1090/S0002-9947-2010-05056-1

Annihilators of graded components of the canonical module, and the core of standard graded algebras
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by Louiza Fouli, Claudia Polini and Bernd Ulrich PDF

Trans. Amer. Math. Soc. 362 (2010), 6183-6203 Request permission

Abstract:

We relate the annihilators of graded components of the canonical module of a graded Cohen-Macaulay ring to colon ideals of powers of the homogeneous maximal ideal. In particular, we connect them to the core of the maximal ideal. An application of our results characterizes Cayley-Bacharach sets of points in terms of the structure of the core of the maximal ideal of their homogeneous coordinate ring. In particular, we show that a scheme is Cayley-Bacharach if and only if the core is a power of the maximal ideal.

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