Nash blowups in prime characteristic
Daniel DuarteCONACyT-Universidad Autónoma de Zacatecas, Mexico
Luis Núñez-BetancourtCentro de Investigación en Matemáticas, Guanajuato, Gto., Mexico
We initiate the study of Nash blowups in prime characteristic. First, we show that a normal variety is non-singular if and only if its Nash blowup is an isomorphism, extending a theorem by A. Nobile. We also study higher Nash blowups, as defined by T. Yasuda. Specifically, we give a characteristic-free proof of a higher version of Nobile’s theorem for quotient varieties and hypersurfaces. We also prove a weaker version for -pure varieties.
Cite this article
Daniel Duarte, Luis Núñez-Betancourt, Nash blowups in prime characteristic. Rev. Mat. Iberoam. 38 (2022), no. 1, pp. 257–267DOI 10.4171/RMI/1278