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Degenerate real hypersurfaces in $\mathbb {C}^2$ with few automorphisms.
- Source :
-
Transactions of the American Mathematical Society . Dec2008, Vol. 361 Issue 6, p3241-3267. 27p. - Publication Year :
- 2008
-
Abstract
- We introduce new biholomorphic invariants for real-analytic hypersurfaces in $mathbb {C}^2$ and show how they can be used to show that a hypersurface possesses few automorphisms. We give conditions, in terms of the new invariants, guaranteeing that the stability group is finite, and give (sharp) bounds on the cardinality of the stability group in this case. We also give a sufficient condition for the stability group to be trivial. The main technical tool developed in this paper is a complete (formal) normal form for a certain class of hypersurfaces. As a byproduct, a complete classification, up to biholomorphic equivalence, of the finite type hypersurfaces in this class is obtained. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00029947
- Volume :
- 361
- Issue :
- 6
- Database :
- Academic Search Index
- Journal :
- Transactions of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 36783704