Nash blowups of toric varieties in prime characteristic

• Duarte, Daniel ^[3] ; Jeffries, Jack ^[1] ; Núñez-Betancourt, Luis ^[2]
  1. [1] University of Nebraska–Lincoln

     University of Nebraska–Lincoln

     Estados Unidos

     
  2. [2] Mathematics Research Center

     Mathematics Research Center

     México

     
  3. [3] Centro de Ciencias Matemáticas, UNAM, Campus Morelia, Morelia, MICH, Mexico

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• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 75, Fasc. 3, 2024, págs. 629-637
• Idioma: inglés
• DOI: 10.1007/s13348-023-00402-y
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• Resumen

  • We initiate the study of the resolution of singularities properties of Nash blowups over fields of prime characteristic. We prove that the iteration of normalized Nash blowups desingularizes normal toric surfaces. We also introduce a prime characteristic version of the logarithmic Jacobian ideal of a toric variety and prove that its blowup coincides with the Nash blowup of the variety. As a consequence, the Nash blowup of a, not necessarily normal, toric variety of arbitrary dimension in prime characteristic can be described combinatorially.