Affine smooth varieties with finite group of automorphisms
The paper concerns automorphism groups of Zariski open subsets of smooth projective varieties \(X\) over \(\mathbb{C}\). The main problems, considered in the paper, are: 1. under what conditions for a divisor \(H \subset X\) the group of automorphisms \(\Aut (X \backslash H)\) is finite; 2. when an automorphism of \(X \backslash H\) can be extended to an automorphism of \(X\); 3. for which subgroup \(G\) of \(\Aut (X)\) does there exist a divisor \(H \subset X\) such that \(\Aut (X \backslash H) = G\). The main answers, given in the paper, to these questions are: Ad 1. \(H\) does not have uniruled components and is a very ample divisor; Ad 2. the same as above; Ad 3. \(G\) finite. There is also many applications of these results to particular cases.
scientific article; zbMATH DE number 703847