Geodesic
Automorphisms of certain affine complements in projective space
Sbornik. Mathematics, Tome 209 (2018) no. 2, pp. 276-289

Voir la notice de l'article provenant de la source Math-Net.Ru

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 $\operatorname{Aut}({\mathbb P}^M\setminus S)$ is trivial. Bibliography: 24 titles.
Keywords: maximal singularity.
Mots-clés : affine complement, birational map 
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     author = {A. V. Pukhlikov},
     title = {Automorphisms of certain affine complements in projective space},
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A. V. Pukhlikov. Automorphisms of certain affine complements in projective space. Sbornik. Mathematics, Tome 209 (2018) no. 2, pp. 276-289. http://geodesic.mathdoc.fr/item/SM_2018_209_2_a7/