Fano hypersurfaces with no finite order birational automorphisms

We use the specialization homomorphism for the birational automorphism group to study finite order birational automorphisms. For a family of varieties over a DVR, we prove that a birational automorphism of order coprime to the residue characteristic cannot specialize to the identity. As an applicati...

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Bibliographic Details
Published in:arXiv.org 2022-08
Main Authors: Chen, Nathan, Ji, Lena, Stapleton, David
Format: Article
Language:English
Subjects:
Automorphisms
Homomorphisms
Hyperspaces
Online Access:Get full text
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Summary:We use the specialization homomorphism for the birational automorphism group to study finite order birational automorphisms. For a family of varieties over a DVR, we prove that a birational automorphism of order coprime to the residue characteristic cannot specialize to the identity. As an application, we show that very general \(n\)-dimensional hypersurfaces of degree \(d \geq 5 \lceil (n+3)/6 \rceil\) have no finite order birational automorphisms.
ISSN:2331-8422