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arXiv · 2208.07396

Fano hypersurfaces with no finite order birational automorphisms

Nathan Chen·Lena Ji·David Stapleton
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Abstract

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.

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Nathan Chen, Lena Ji, David Stapleton. 2022-08-15. Fano hypersurfaces with no finite order birational automorphisms. https://arxiv.org/abs/2208.07396

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