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AbstractFor each non-negative integernwe define thenth Nash blowup of an algebraic variety, and call them all higher Nash blowups. Whenn=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 itsnth Nash blowup withnlarge enough. Moreover, we completely determine for whichnthenth Nash blowup of an analytically irreducible curve singularity in characteristic zero is normal, in termsdoi:10.1112/s0010437x0700276x fatcat:sixy7ggiorcp3ogbdqq6u33fke