Multiplicities and log canonical threshold
Algebraic Geometry
2007-05-23 v1
Abstract
If R is a local ring of dimension n, of a smooth complex variety, and if I is a zero dimensional ideal in R, then we prove that e(I)\geq n^n/lc(I)^n. Here e(I) is the Samuel multiplicity along I, and lc(I) is the log canonical threshold of (R,I). We show that equality is achieved if and only if the integral closure of I is a power of the maximal ideal. When I is an arbitrary ideal, but n=2, we give a similar bound involving the Segre numbers of I.
Cite
@article{arxiv.math/0205171,
title = {Multiplicities and log canonical threshold},
author = {Tommaso de Fernex and Lawrence Ein and Mircea Mustata},
journal= {arXiv preprint arXiv:math/0205171},
year = {2007}
}
Comments
13 pages; AMS-LaTeX