Automorphisms of cubic surfaces without points

Constantin Shramov

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arXiv · 2006.02531

Automorphisms of cubic surfaces without points

Constantin Shramov

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Abstract

We classify finite groups acting by birational transformations of a non-trivial Severi--Brauer surface over a field of characteristc zero that are not conjugate to subgroups of the automorphism group. Also, we show that the automorphism group of a smooth cubic surface over a field $K$ of characteristic zero that has no $K$-points is abelian, and find a sharp bound for the Jordan constants of birational automorphism groups of such cubic surfaces.

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Constantin Shramov. 2020-06-03. Automorphisms of cubic surfaces without points. https://arxiv.org/abs/2006.02531

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