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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Local cohomology of Rees algebras and Hilbert functions


Authors: Bernard Johnston and Jugal Verma
Journal: Proc. Amer. Math. Soc. 123 (1995), 1-10
MSC: Primary 13D45; Secondary 13A30, 13D40
MathSciNet review: 1217453
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Abstract: Let I be an ideal primary to the maximal ideal in a local ring. We utilize two well-known theorems due to J.-P. Serre to prove that the difference between the Hilbert function and the Hilbert polynomial of I is the alternating sum of the graded pieces of the graded local cohomology (with respect to its positively-graded ideal) of the Rees ring of I. This gives new insight into the higher Hilbert coefficients of I. The result is inspired by one due to J. D. Sally in dimension two and is implicit in a paper by D. Kirby and H. A. Mehran, where very different methods are used.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1995-1217453-X
PII: S 0002-9939(1995)1217453-X
Keywords: Hilbert polynomial, local cohomology, Rees ring
Article copyright: © Copyright 1995 American Mathematical Society