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Ordinary Singularities with Decreasing Hilbert Function

Published online by Cambridge University Press:  20 November 2018

Leslie G. Roberts
Leslie G. Roberts*
Affiliation:
Queen's University, Kingston, Ontario
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Let A be the co-ordinate ring of a reduced curve over a field k. This means that A is an algebra of finite type over k, A has no nilpotent elements, and that if P is a minimal prime ideal of A, then A/P is an integral domain of Krull dimension one. Let M be a maximal ideal of A. Then G(A) (the graded ring of A relative to M) is defined to be . We get the same graded ring if we first localize at M, and then form the graded ring of AM relative to the maximal ideal MAM. That is

Let Ā be the integral closure of A. If P 1, P 2, …, Ps are the minimal primes of A then

where A/Pi is a domain and is the integral closure of A/Pi in its quotient field.

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 34 , Issue 1 , 01 February 1982, pp. 169 - 180
Copyright
Copyright © Canadian Mathematical Society 1982

References

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