Del Pezzo surfaces and Mori fiber spaces in positive characteristic
Algebraic Geometry
2021-10-04 v2
Abstract
We settle a question that originates from results and remarks by Koll\'ar on extremal ray in the minimal model program: In positive characteristics, there are no Mori fibrations on threefolds with only terminal singularities whose generic fibers are geometrically non-normal surfaces. To show this we establish some general structure results for del Pezzo surfaces over imperfect ground fields. This relies on Reid's classification of non-normal del Pezzo surfaces over algebraically closed fields, combined with a detailed analysis of geometrical non-reducedness over imperfect fields of p-degree one.
Keywords
Cite
@article{arxiv.1802.08436,
title = {Del Pezzo surfaces and Mori fiber spaces in positive characteristic},
author = {Andrea Fanelli and Stefan Schröer},
journal= {arXiv preprint arXiv:1802.08436},
year = {2021}
}
Comments
71 pages, minor changes, to appear in Trans. Amer. Math. Soc