Local equivalence of symmetric hypersurfaces in $\mathbb C^2$

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dc.creatorKolar, Martin
dc.date2007-09-21
dc.date.accessioned2026-07-07T08:31:26Z
dc.date.available2026-07-07T08:31:26Z
dc.descriptionThe 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 $\mathbb C^2$. 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.
dc.identifierhttps://arxiv.org/abs/0709.3374
dc.identifierhttp://arxiv.org/abs/0709.3374
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/138501
dc.subjectComplex Variables
dc.subject32V35, 32V40, 32T25
dc.titleLocal equivalence of symmetric hypersurfaces in $\mathbb C^2$
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