Higher Nash blowups

Takehiko Yasuda

doi:10.1112/S0010437X0700276X

Higher Nash blowups

Algebraic Geometry 2024-02-27 v3

Authors: Takehiko Yasuda

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Abstract

For each non-negative integer $n$ , we define the $n$ -th 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 $n$ -th Nash blowup with $n$ large enough.

Keywords

blow-up

Cite

@article{arxiv.math/0512184,
  title  = {Higher Nash blowups},
  author = {Takehiko Yasuda},
  journal= {arXiv preprint arXiv:math/0512184},
  year   = {2024}
}

Comments

23 pages;v.3, major revision. The definition of higher Nash blowups has been modified. The new definition coincides with the previous one in characteristic zero. Main results have been generalized. In particular, the conjecture in the paper has been proved for curves

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