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arXiv · 1705.06331

Global smoothing of a subanalytic set

Edward Bierstone·Adam Parusinski
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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 fibres 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 Parusinski. 2017-05-17. Global smoothing of a subanalytic set. https://doi.org/10.1215/00127094-2018-0032

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