Multiplicities and log canonical threshold

Details Multiplicities and log canonical threshold Multiplicities and log canonical threshold

2002-05-15

arxiv.org/abs/math/0205171v1

J. Alg. Geom. 13 (2004), 603-615.

Mathematics

Algebraic Geometry

13 pages; AMS-LaTeX

Scientific paper

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.

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