Annihilators of Graded Components of the Canonical Module, and the Core of Standard Graded Algebras

Details Annihilators of Graded Components of the Canonical Module, and the Core of Standard Graded Algebras Annihilators of Graded Components of the Canonical Module, and the Core of Standard Graded Algebras

2009-03-19

arxiv.org/abs/0903.3439v1

Mathematics

Commutative Algebra

21 pages, to appear in Transactions of the AMS

Scientific paper

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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