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ON DEL PEZZO FIBRATIONS IN POSITIVE CHARACTERISTIC

Part of: Arithmetic problems. Diophantine geometry Surfaces and higher-dimensional varieties Birational geometry

Published online by Cambridge University Press:  30 March 2020

Fabio Bernasconi Open the ORCID record for Fabio Bernasconi [Opens in a new window]  and
Hiromu Tanaka
Fabio Bernasconi
Affiliation:
Department of Mathematics, University of Utah, Salt Lake City, UT 84112, USA (fabio@math.utah.edu)
Hiromu Tanaka
Affiliation:
Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo153-8914, Japan (tanaka@ms.u-tokyo.ac.jp)
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Abstract

We establish two results on three-dimensional del Pezzo fibrations in positive characteristic. First, we give an explicit bound for torsion index of relatively torsion line bundles. Second, we show the existence of purely inseparable sections with explicit bounded degree. To prove these results, we study log del Pezzo surfaces defined over imperfect fields.

Keywords

minimal model programgeneric fibresdel Pezzo surfacespositive characteristic

MSC classification

Primary: 14E30: Minimal model program (Mori theory, extremal rays) 14G17: Positive characteristic ground fields 14J45: Fano varieties
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 21 , Issue 1 , January 2022 , pp. 197 - 239
Copyright
© The Author(s) 2020. Published by Cambridge University Press

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