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Higher Nash blowups

Part of: Local theory Birational geometry

Published online by Cambridge University Press:  01 November 2007

Takehiko Yasuda
Takehiko Yasuda*
Affiliation:
Research Institute for Mathematical Sciences, Kyoto University, Kyoto, 606-8502, Japan (email: takehiko@kurims.kyoto-u.ac.jp)
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Abstract

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For each non-negative integer n we define the nth Nash blowup of an algebraic variety, and call them all higher Nash blowups. When n=1, it coincides with the classical Nash blowup. We study higher Nash blowups of curves in detail and prove that any curve in characteristic zero can be desingularized by its nth Nash blowup with n large enough. Moreover, we completely determine for which n the nth Nash blowup of an analytically irreducible curve singularity in characteristic zero is normal, in terms of the associated numerical monoid.

Keywords

Nash blowupresolution of singularitiesHilbert scheme of points

MSC classification

Secondary: 14E15: Global theory and resolution of singularities 14B12: Local deformation theory, Artin approximation, etc.
Type
Research Article
Information
Compositio Mathematica , Volume 143 , Issue 6 , November 2007 , pp. 1493 - 1510
Copyright
Copyright © Foundation Compositio Mathematica 2007