English

Global smoothing of a subanalytic set

Complex Variables 2018-11-14 v2 Algebraic Geometry

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.

Keywords

Cite

@article{arxiv.1705.06331,
  title  = {Global smoothing of a subanalytic set},
  author = {Edward Bierstone and Adam Parusinski},
  journal= {arXiv preprint arXiv:1705.06331},
  year   = {2018}
}

Comments

11 pages, to appear in Duke Math. J

R2 v1 2026-06-22T19:50:26.223Z