Irreducible identity sets for polynomial automorphisms
The author studies polynomial automorphisms of algebraic, affine and projective, varieties over \(\mathbb{C}\). First, he proves that every \((n-1)\)- dimensional component of the set of fixed points of a polynomial automorphism of \(\mathbb{C}^ n\) is uniruled at infinity. Second, he gives classes of hypersurfaces which are identity sets for polynomial automorphisms and sets determining polynomial automorphisms of \(\mathbb{C}^ n\), respectively. Third, he gives classes of hypersurfaces \(V\) in projective manifolds \(X\) (in particular in \(\mathbb{P}^ n (\mathbb{C})\) and \(\mathbb{C}^ n)\) for which every polynomial automorphism of the set \(X \backslash V\) can be extended to a polynomial automorphism of \(X\).
scientific article; zbMATH DE number 549754
scientific article