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arXiv · 1704.00018

Automorphisms of certain affine complements in the projective space

Aleksandr V. Pukhlikov
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Abstract

We prove that every biregular automorphism of the affine algebraic variety ${\mathbb P}^M\setminus S$, $M\geqslant 3$, where $S\subset {\mathbb P}^M$ is a hypersurface of degree $m\geqslant M+1$ with a unique singular point of multiplicity $(m-1)$, resolved by one blow up, is a restriction of some automorphism of the projective space ${\mathbb P}^M$, preserving the hypersurface $S$; in particular, for a general hypersurface $S$ the group $\mathop{\rm Aut} ({\mathbb P}^M\setminus S)$ is trivial.

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Aleksandr V. Pukhlikov. 2017-03-31. Automorphisms of certain affine complements in the projective space. https://doi.org/10.1070/sm8839

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