Multiplicities of graded components of local cohomology modules
- Brodmann, M.
- Rohrer, F.
- Sazeedeh, R.
DOIAbstract
AbstractLet M be a finitely generated graded module over a Noetherian homogeneous ring R with local base ring (R0,m0). Then, the nth graded component HR+i(M)n of the ith local cohomology module of M with respect to the irrelevant ideal R+ of R is a finitely generated R0-module which vanishes for all n≫0. In various situations we show that, for an m0-primary ideal q0⊆R0, the multiplicity eq0(HR+i(M)n) of HR+i(M)n is antipolynomial in n of degree less than i. In particular we consider the following three cases:(a)i<g(M), where g(M) is the so-called cohomological finite length dimension of M;(b)i=g(M);(c)dim(R0)=2.In cases (a) and (b) we express the degree and the leading coefficient of the representing polynomial in terms of local cohomologic...
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