Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Cayley-Bacharach schemes and their canonical modules


Authors: Anthony V. Geramita, Martin Kreuzer and Lorenzo Robbiano
Journal: Trans. Amer. Math. Soc. 339 (1993), 163-189
MSC: Primary 14M05; Secondary 13D40
MathSciNet review: 1102886
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A set of $ s$ points in $ {\mathbb{P}^d}$ is called a Cayley-Bacharach scheme ( $ {\text{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 $ {\text{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 $ {\text{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 $ {\text{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 $ {\text{CB}}$-scheme, results about generic hyperplane sections of arithmetically Cohen-Macaulay curves and inequalities for the Hilbert functions of Cohen-Macaulay domains.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 14M05, 13D40

Retrieve articles in all journals with MSC: 14M05, 13D40


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1993-1102886-5
PII: S 0002-9947(1993)1102886-5
Article copyright: © Copyright 1993 American Mathematical Society