On the last Hilbert-Samuel coefficient of isolated singularities
Commutative Algebra
2010-11-05 v1 Algebraic Geometry
Abstract
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.
Keywords
Cite
@article{arxiv.1011.0846,
title = {On the last Hilbert-Samuel coefficient of isolated singularities},
author = {Juan Elias},
journal= {arXiv preprint arXiv:1011.0846},
year = {2010}
}