Multiplicities and log canonical threshold

de Fernex, Tommaso; Ein, Lawrence; Mustata, Mircea

Multiplicities and log canonical threshold

Authors

de Fernex, Tommaso

Ein, Lawrence

Mustata, Mircea

Description

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.
13 pages; AMS-LaTeX