Universal flattening of Frobenius

Details Universal flattening of Frobenius Universal flattening of Frobenius

2007-06-19

arxiv.org/abs/0706.2700v5

Mathematics

Algebraic Geometry

25 pages; v4. a full revision, notations changed, the isomorphism of the F-blowup and the G-Hilbert scheme has been generalize

Scientific paper

For a variety $X$ of positive characteristic and a non-negative 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 non-negative 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.

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