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arXiv · 1802.08436

Del Pezzo surfaces and Mori fiber spaces in positive characteristic

Andrea Fanelli·Stefan Schröer
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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.

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Andrea Fanelli, Stefan Schröer. 2018-02-23. Del Pezzo surfaces and Mori fiber spaces in positive characteristic. https://arxiv.org/abs/1802.08436

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