  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.
