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1 June 2006 A numerical criterion for simultaneous normalization
Hung-Jen Chiang-Hsieh, Joseph Lipman
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Duke Math. J. 133(2): 347-390 (1 June 2006). DOI: 10.1215/S0012-7094-06-13327-6

Abstract

We investigate conditions for simultaneous normalizability of a family of reduced schemes; that is, the normalization of the total space normalizes, fiber by fiber, each member of the family. The main result (under more general conditions) is that a flat family of reduced equidimensional projective C-varieties (Xy)yY with normal parameter space Y—algebraic or analytic—admits a simultaneous normalization if and only if the Hilbert polynomial of the integral closure OXy̲ is locally independent of y. When the Xy are curves, projectivity is not needed, and the statement reduces to the well-known δ-constant criterion ofTeissier. The proofs are basically algebraic, analytic results being related via standard techniques (Stein compacta and forth) to more abstract algebraic ones

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Hung-Jen Chiang-Hsieh. Joseph Lipman. "A numerical criterion for simultaneous normalization." Duke Math. J. 133 (2) 347 - 390, 1 June 2006. https://doi.org/10.1215/S0012-7094-06-13327-6

Information

Published: 1 June 2006
First available in Project Euclid: 21 May 2006

zbMATH: 1101.14004
MathSciNet: MR2225697
Digital Object Identifier: 10.1215/S0012-7094-06-13327-6

Subjects:
Primary: 14B05, 32S15

Rights: Copyright © 2006 Duke University Press

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Vol.133 • No. 2 • 1 June 2006
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