GERAMITA, AV and KREUZER, M and ROBBIANO, L (1993) CAYLEY-BACHARACH SCHEMES AND THEIR CANONICAL MODULES. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 339 (1). pp. 163-189. ISSN 0002-9947,
Full text not available from this repository.Abstract
A set of s points in P(d) is called a Cayley-Bacharach scheme (CB-scheme), if every subset of s - 1 points has the same Hilbert function. We investigate the consequences of this ''weak uniformity.'' The main result characterizes CB-schemes in terms of the structure of the canonical module of their projective coordinate ring. From this we get that the Hilbert function of a CB-scheme X has to satisfy growth conditions which are only slightly weaker than the ones given by Harris and Eisenbud for points with the uniform position property. We also characterize CB-schemes in terms of the conductor of the projective coordinate ring in its integral closure and in terms of the forms of minimal degree passing through a linked set of points. Applications include efficient algorithms for checking whether a given set of points is a CB-scheme, results about generic hyperplane sections of arithmetically Cohen-Macaulay curves and inequalities for the Hilbert functions of Cohen-Macaulay domains.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | CURVES; SECTIONS; |
| Depositing User: | Dr. Gernot Deinzer |
| Last Modified: | 19 Oct 2022 08:42 |
| URI: | https://pred.uni-regensburg.de/id/eprint/53817 |
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