Universal flattening of Frobenius

• Autores: Takehiko Yasuda
• Localización: American journal of mathematics, ISSN 0002-9327, Vol. 134, Nº 2, 2012, págs. 349-378
• Idioma: inglés
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• Resumen

  • For a variety $X$ of positive characteristic and a nonnegative integer $e$, we define its $e$-th F-blowup to be the universal flattening of the $e$-iterated Frobenius of $X$. Thus we have the sequence (a set labeled by nonnegative integers) of blowups of $X$. Under some condition, the sequence stabilizes and leads to a nice (for instance, minimal or crepant) resolution. For tame quotient singularities, the sequence leads to the $G$-Hilbert scheme.