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Some applications of the canonical module of a $$0$$-dimensional scheme. (English) Zbl 0826.14031
Orecchia, Ferruccio (ed.) et al., Zero-dimensional schemes. Proceedings of the international conference held in Ravello, Italy, June 8-13, 1992. Berlin: de Gruyter. 243-252 (1994).
The author [in: Can. J. Math. 46, No. 2, 357-379 (1994; see the preceding review)] defined several kinds of uniformities for a 0-dimensional subscheme $$Z$$ of $$\mathbb{P}^d$$ generalizing the classical Cayley-Bacharach property of general hyperplane sections of an integral curve of $$\mathbb{P}^{d + 1}$$ (in characteristic 0). Here, as well in the author’s joint paper with L. Robbiano, “On maximal Cayley-Bacharach schemes” [Commun. Algebra 23, No. 9, 3357-3378 (1995)] and the references quoted there the author studies $$Z$$ with algebraic tools (local duality and the canonical module). His results are applied here also to the study of combinatorial properties (“purity”, “flawless”) of the Hilbert function of $$Z$$.
For the entire collection see [Zbl 0797.00007].
Reviewer: E.Ballico (Povo)

##### MSC:
 14M05 Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal) 14N05 Projective techniques in algebraic geometry 14H50 Plane and space curves 14C17 Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry