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.References
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Additional Information
- Andrea Fanelli
- Affiliation: Institut de Mathématiques de Bordeaux, CNRS UMR 5251, Université de Bordeaux, 33405 Talence Cedex, France
- MR Author ID: 1126251
- Email: andrea.fanelli.1@u-bordeaux.fr
- Stefan Schröer
- Affiliation: Mathematisches Institut, Heinrich-Heine-Universität, 40204 Düsseldorf, Germany
- MR Author ID: 630946
- Email: schroeer@math.uni-duesseldorf.de
- Received by editor(s): December 11, 2018
- Received by editor(s) in revised form: June 25, 2019
- Published electronically: December 17, 2019
- Additional Notes: The first author was funded by the Deutsche Forschungsgemeinschaft with the grant PE 2165/1-2 Gromov-Witten Theorie, Geometrie und Darstellungen.
- © Copyright 2019 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 373 (2020), 1775-1843
- MSC (2010): Primary 14E30, 14G17, 14J26, 14J30, 14J17, 14H20, 14J45
- DOI: https://doi.org/10.1090/tran/7988
- MathSciNet review: 4068282