English

Universal flattening of Frobenius

Algebraic Geometry 2024-02-27 v5 Commutative Algebra

Abstract

For a variety XX of positive characteristic and a non-negative integer ee, we define its ee-th F-blowup to be the universal flattening of the ee-iterated Frobenius of XX. Thus we have the sequence (a set labeled by non-negative integers) of blowups of XX. 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 GG-Hilbert scheme.

Keywords

Cite

@article{arxiv.0706.2700,
  title  = {Universal flattening of Frobenius},
  author = {Takehiko Yasuda},
  journal= {arXiv preprint arXiv:0706.2700},
  year   = {2024}
}
R2 v1 2026-06-21T08:39:42.239Z