Automorphisms of certain affine complements in the projective space

Abstract

We prove that every biregular automorphism of the affine algebraic variety ${\mathbb{P}}^M\setminus S$, $M⩾3$, where $S\subset {\mathbb{P}}^M$ is a hypersurface of degree $m⩾M+1$ 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 $\mathrm{Aut}({\mathbb{P}}^M\setminus S)$ is trivial.

15 pages

Cited by in corpus (2)

• Super-rigid Affine Fano Varieties
• Affine complements in the projective space with the trivial group of automorphisms