Multiplicities and log canonical threshold

Authors:
Tommaso de Fernex, Lawrence Ein and Mircea Mustata

Translated by:

Journal:
J. Algebraic Geom. **13** (2004), 603-615

DOI:
https://doi.org/10.1090/S1056-3911-04-00346-7

Published electronically:
February 25, 2004

MathSciNet review:
2047683

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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 .

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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

DOI:
https://doi.org/10.1090/S1056-3911-04-00346-7

Received by editor(s):
May 23, 2002

Published electronically:
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.