Automorphism groups of rigid affine surfaces: the identity component

Autor:	Perepechko, Alexander, Zaidenberg, Mikhail
Rok vydání:	2022
Předmět:	Mathematics - Algebraic Geometry 14J50 14R20 (primary) 14L30 05C60 (secondary)
Druh dokumentu:	Working Paper
Popis:	It is known that the identity component of the automorphism group of a projective algebraic variety is an algebraic group. This is not true in general for quasi-projective varieties. In this note we address the question: given an affine algebraic surface $Y$, as to when the identity component ${\rm Aut}^0 (Y)$ of the automorphism group ${\rm Aut} (Y)$ is an algebraic group? We show that this happens if and only if $Y$ admits no effective action of the additive group. In the latter case, ${\rm Aut}^0 (Y)$ is an algebraic torus of rank $\le 2$. Comment: 30 pages, 3 figures; the Introduction extended, references and acknowledgments added
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2208.09738 Zobrazit plný text záznamu View this record from Arxiv