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@article{876396, author = {Kolář, Martin}, article_location = {Providence (USA)}, article_number = {6}, keywords = {Normal forms; Levi degenerate manifolds; finite type}, language = {eng}, issn = {0002-9947}, journal = {Transactions of the American Mathematical Society}, title = {Local equivalence of symmetric hypersurfaces in C^2}, volume = {362}, year = {2010} }
TY - JOUR ID - 876396 AU - Kolář, Martin PY - 2010 TI - Local equivalence of symmetric hypersurfaces in C^2 JF - Transactions of the American Mathematical Society VL - 362 IS - 6 SP - 2833-2843 EP - 2833-2843 PB - American Mathematical Society SN - 00029947 KW - Normal forms KW - Levi degenerate manifolds KW - finite type N2 - 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{C}^2$. The results give complete normalizations for such hypersurfaces, which respect 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. Similar results for hypersurfaces admitting nontransversal symmetries are obtained. ER -
KOLÁŘ, Martin. Local equivalence of symmetric hypersurfaces in C\^{}2. \textit{Transactions of the American Mathematical Society}. Providence (USA): American Mathematical Society, roč.~362, č.~6, s.~2833-2843. ISSN~0002-9947. 2010.
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