Automorphism groups of rational elliptic and quasi-elliptic surfaces in all characteristics

We study the groups of automorphisms of rational algebraic surfaces that admit a relatively minimal pencil of curves of arithmetic genus one over an algebraically closed field of arbitrary characteristic. In particular, we classify such surfaces that admit non-trivial automorphisms that act triviall...

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Bibliographic Details
Published in:arXiv.org 2021-06
Main Authors: Dolgachev, Igor, Gebhard, Martin
Format: Article
Language:English
Subjects:
Automorphisms
Classification
Online Access:Get full text
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Summary:We study the groups of automorphisms of rational algebraic surfaces that admit a relatively minimal pencil of curves of arithmetic genus one over an algebraically closed field of arbitrary characteristic. In particular, we classify such surfaces that admit non-trivial automorphisms that act trivially on the Picard group. As an application, we classify classical Enriques surfaces in characteristic \(2\) that admit non-trivial numerically trivial automorphisms.
ISSN:2331-8422