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Title: Degenerate real hypersurfaces in C2 with few automorphisms
Sponsor: Science Foundation Ireland
Author's Homepage:
Keywords: Pure & Applied Mathematics
Issue Date: 2009
Citation: P. Ebenfelt, B. Lamel, D. Zaitsev, Degenerate real hypersurfaces in C2 with few automorphisms, Trans. Amer. Math. Soc, 361, 6, 2009, 3241-3267
Series/Report no.: Trans. Amer. Math. Soc
Abstract: We introduce new biholomorphic invariants for real-analytic hypersurfaces in 2-dimensional complex space 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.
Description: PUBLISHED
Appears in Collections:Pure & Applied Mathematics (Scholarly Publications)

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