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Pré-Publication, Document De Travail (Preprint/Prepublication) Année : 2022

AUTOMORPHISM GROUPS OF RIGID AFFINE SURFACES: THE IDENTITY COMPONENT

M Zaidenberg

Résumé

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 Aut • (Y) of the automorphism group 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, Aut • (Y) is an algebraic torus of rank ≤ 2.
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Dates et versions

hal-03848662 , version 1 (10-11-2022)

Identifiants

  • HAL Id : hal-03848662 , version 1

Citer

Alexander Perepechko, M Zaidenberg. AUTOMORPHISM GROUPS OF RIGID AFFINE SURFACES: THE IDENTITY COMPONENT. 2022. ⟨hal-03848662⟩

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