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Annihilators of graded components of the canonical module, and the core of standard graded algebras
Author(s):
Louiza
Fouli;
Claudia
Polini;
Bernd
Ulrich
Journal:
Trans. Amer. Math. Soc.
362
(2010),
6183-6203.
MSC (2010):
Primary 13B21;
Secondary 13A30, 13B22, 13C40
Posted:
July 22, 2010
MathSciNet review:
2678970
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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.
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Additional Information:
Louiza
Fouli
Affiliation:
Department of Mathematical Sciences, New Mexico State University, Las Cruces, New Mexico 88003
Email:
lfouli@math.nmsu.edu
Claudia
Polini
Affiliation:
Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556
Email:
cpolini@nd.edu
Bernd
Ulrich
Affiliation:
Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
Email:
ulrich@math.purdue.edu
DOI:
10.1090/S0002-9947-2010-05056-1
PII:
S 0002-9947(2010)05056-1
Received by editor(s):
August 14, 2007
Posted:
July 22, 2010
Additional Notes:
The second and third author gratefully acknowledge partial support from the NSF. The second author was also supported in part by the NSA. The first and second author thank the Department of Mathematics of Purdue University for its hospitality
Copyright of article:
Copyright
2010,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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