Irreducible identity sets for polynomial automorphisms. (English) Zbl 0806.14011
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 \(X\).
Reviewer: T.Krasiński (Łódź)
MSC:
| 14J50 | Automorphisms of surfaces and higher-dimensional varieties |
| 32H25 | Picard-type theorems and generalizations for several complex variables |
| 14J26 | Rational and ruled surfaces |
| 13F20 | Polynomial rings and ideals; rings of integer-valued polynomials |
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