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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)

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
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