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Asymptotic behaviour of the length of local cohomology

Steven Dale Cutkosky·Huy Tai Ha·Hema Srinivasan·Emanoil Theodorescu
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Abstract

Let k be a field of characteristic 0, R = k[x_1, ..., x_d] be a polynomial ring, and m its maximal homogeneous ideal. Let I be a homogeneous ideal in R. In this paper we investigate asymptotic behaviour of the quotient between the length of local cohomology group H^0_m(R/I^n) and n^d. We show that this quantity always has a limit as n goes to infinity. We also give an example for which the limit is irrational; in particular, this proves that the length of H^0_m(R/I^n) is not asymptotically a polynomial in n.

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Steven Dale Cutkosky, Huy Tai Ha, Hema Srinivasan, Emanoil Theodorescu. 2004-03-22. Asymptotic behaviour of the length of local cohomology. https://arxiv.org/abs/math/0403370

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