Annihilators of graded components of the canonical module, and the core of standard graded algebras. (English) Zbl 1210.13012
Authors’ 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.
Reviewer: Gyu Whan Chang (Incheon)
MSC:
| 13B21 | Integral dependence in commutative rings; going up, going down |
| 13A30 | Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics |
| 13B22 | Integral closure of commutative rings and ideals |
| 13C40 | Linkage, complete intersections and determinantal ideals |
| 13A02 | Graded rings |
Keywords:
Standard graded Cohen-Macaulay algebra \(R\) over a field; graded canonical module \(\omega\) of \(R\); annihilators of graded components of \(\omega\); homogeneous maximal ideal; core of an idealReferences:
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