Del Pezzo surfaces and Mori fiber spaces in positive characteristic

Fanelli, Andrea; Schröer, Stefan

doi:10.1090/tran/7988

Del Pezzo surfaces and Mori fiber spaces in positive characteristic
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by Andrea Fanelli and Stefan Schröer PDF

Trans. Amer. Math. Soc. 373 (2020), 1775-1843 Request permission

Abstract:

We settle a question that originates from results and remarks by Kollár on extremal rays 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.

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