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1 November 2018 Global smoothing of a subanalytic set
Edward Bierstone, Adam Parusiński
Duke Math. J. 167(16): 3115-3128 (1 November 2018). DOI: 10.1215/00127094-2018-0032

Abstract

We give rather simple answers to two long-standing questions in real-analytic geometry, on global smoothing of a subanalytic set, and on transformation of a proper real-analytic mapping to a mapping with equidimensional fibers by global blowings-up of the target. These questions are related: a positive answer to the second can be used to reduce the first to the simpler semianalytic case. We show that the second question has a negative answer, in general, and that the first problem nevertheless has a positive solution.

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Edward Bierstone. Adam Parusiński. "Global smoothing of a subanalytic set." Duke Math. J. 167 (16) 3115 - 3128, 1 November 2018. https://doi.org/10.1215/00127094-2018-0032

Information

Received: 16 June 2017; Revised: 29 May 2018; Published: 1 November 2018
First available in Project Euclid: 3 October 2018

zbMATH: 06985302
MathSciNet: MR3870082
Digital Object Identifier: 10.1215/00127094-2018-0032

Subjects:
Primary: 32B20
Secondary: 14B25 , 14E15 , 14P10 , 14P15 , 32C05 , 32S45

Keywords: local flattener , resolution of singularities , semialgebraic set , subanalytic set

Rights: Copyright © 2018 Duke University Press

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Vol.167 • No. 16 • 1 November 2018
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