Takehiko Yasuda
Published 2005-12-09, updated 2006-04-17Version 3
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.
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
On algorithmic unsolvability of the problem embeddability of algebraic varieties over a field of characteristic zero
Strong resolution of singularities in characteristic zero
Lagrangian geometry of algebraic varieties
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