Counterexamples to the MMP for 1-foliations in positive characteristic

Fabio Bernasconi

Counterexamples to the MMP for 1-foliations in positive characteristic

Algebraic Geometry 2024-01-10 v2

Authors: Fabio Bernasconi

Abstract

We show that many statements of the Minimal Model Program, including the cone theorem, the base point free theorem and the existence of Mori fibre spaces, fail for 1-foliated surface pairs $(X,\mathcal{F})$ with canonical singularities in characteristic $p>0$ .

Keywords

minimal model program 1-foliations positive characteristic canonical singularities cone theorem Mori fibre spaces

Cite

@article{arxiv.2309.13978,
  title  = {Counterexamples to the MMP for 1-foliations in positive characteristic},
  author = {Fabio Bernasconi},
  journal= {arXiv preprint arXiv:2309.13978},
  year   = {2024}
}

Comments

9 pages, minor corrections. To appear in the Edge volume at Ann. Univ. Ferrara

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