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Multiplicities and log canonical threshold
Author(s):
Tommaso
de Fernex;
Lawrence
Ein;
Mircea
Mustata
Journal:
J. Algebraic Geom.
13
(2004),
603-615.
Posted:
February 25, 2004
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Abstract |
References |
Additional information
Abstract:
Given an  -dimensional local ring  of a smooth variety, and a zero-dimensional ideal  , we prove the following inequality involving the Samuel multiplicity and the log canonical threshold:  . Moreover, equality holds if and only if the integral closure of  is a power of the maximal ideal in  . When  , we give a similar inequality for an arbitrary ideal  .
References:
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Additional Information:
Tommaso
de Fernex
Affiliation:
Department of Mathematics, University of Michigan, 525 East University Avenue, Ann Arbor, Michigan 48109-1109
Email:
defernex@math.uic.edu
Lawrence
Ein
Affiliation:
Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, 851 Morgan St., M/C. 249, Chicago, Illinois 60607-7045
Email:
ein@math.uic.edu
Mircea
Mustata
Affiliation:
Department of Mathematics, Harvard University, One Oxford Street, Cambridge, Massachusetts 02138
Email:
mirceamustata@yahoo.com
PII:
S 1056-3911(04)00346-7
Received by editor(s):
May 23, 2002
Posted:
February 25, 2004
Additional Notes:
Research of the first author was partially supported by MURST of Italian Government, National Research Project (Cofin 2000) ``Geometry of Algebraic Varieties''. Research of the second author was partially supported by NSF Grant DMS~99-70295. The third author served as a Clay Mathematics Institute Long-Term Prize Fellow while this research was done.
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