Higher Nash blowups

Takehiko Yasuda

Research output: Contribution to journalArticlepeer-review

15 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)1493-1510
Number of pages18
JournalCompositio Mathematica
Issue number6
Publication statusPublished - 2007 Nov


  • Hilbert scheme of points
  • Nash blowup
  • Resolution of singularities

ASJC Scopus subject areas

  • Algebra and Number Theory


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