Groups acting on cubic surfaces in characteristic zero

Name: Groups acting on cubic surfaces in characteristic zero
Creator: Smith, Jonathan M.
Keywords: 14J50, 14J45, 14E08, Mathematics - Algebraic Geometry, Fano varieties, Automorphisms of surfaces and higher-dimensional varieties, Rationality questions in algebraic geometry

Smith, Jonathan M.

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Article . 2025 . Peer-reviewed

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Article . 2025

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Groups acting on cubic surfaces in characteristic zero

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 29 Jan 2025 English Publisher:American Mathematical Society (AMS)Journal:Proceedings of the American Mathematical Society, volume 153, pages 1,025-1,040 (issn: 0002-9939, eissn: 1088-6826,

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Authors: Smith, Jonathan M.;

doi: 10.1090/proc/17090

arXiv: 2401.15735

Groups acting on cubic surfaces in characteristic zero

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Abstract

For every field k k of characteristic zero, we determine the groups that act as automorphisms on a smooth cubic surface over k k . We also determine the groups that act on k k -rational, stably k k -rational, or k k -unirational smooth cubic surfaces.

Keywords

14J50, 14J45, 14E08, Mathematics - Algebraic Geometry, Fano varieties, Automorphisms of surfaces and higher-dimensional varieties, Rationality questions in algebraic geometry

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