On the last Hilbert-Samuel coefficient of isolated singularities

Details On the last Hilbert-Samuel coefficient of isolated singularities On the last Hilbert-Samuel coefficient of isolated singularities

2010-11-03

arxiv.org/abs/1011.0846v1

Mathematics

Commutative Algebra

Scientific paper

In 1978 Lipman presented a proof of the existence of a desingularization for any excellent surface. The strategy of Lipman's proof is based on the finiteness of the number H(R) defined as the supreme of the second Hilbert-Samuel coefficient I, where I range the set of normal m-primary ideals of a Noetherian complete local ring (R,m). The problem studied in the paper is the extension of the result of Lipman on H(R) to m-primary ideals I of a d-dimensional Cohen-Macaulay ring R such that the associated graded ring of R with respect to I^n is Cohen-Macaulay for n>> 0.

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