Local equivalence of symmetric hypersurfaces in \mathbb C²

2007/09/21 by Martin Kolar, Martin Kolář, Kolar, Martin
Mathematics · #Advanced Algebra and Geometry #Geometric and Algebraic Topology #Holomorphic and Operator Theory #math.CV #msc:32T25 #msc:32V35 #msc:32V40

paper · pdf · doi:10.48550/arxiv.0709.3374

arxiv created 2007/09/21 · arxiv updated 2009/12/01

Abstract

The Chern-Moser normal form and its analog on finite type hypersurfaces in general do not respect symmetries. Extending the work of N. K. Stanton, we consider the local equivalence problem for symmetric Levi degenerate hypersurfaces of finite type in \mathbb C². The results give for all such hypersurfaces a complete normalization which respects the symmetries. In particular, they apply to tubes and rigid hypersurfaces, providing an effective classification. The main tool is a complete normal form constructed for a general hypersurface with a tube model. As an application, we describe all biholomorphic maps between tubes, answering a question posed by N. Hanges.

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