Higher order symmetries of real hypersurfaces in $\mathbb C^3$
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- by Martin Kolar and Francine Meylan
- Proc. Amer. Math. Soc. 144 (2016), 4807-4818
- DOI: https://doi.org/10.1090/proc/13090
- Published electronically: April 25, 2016
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Abstract:
We study nonlinear automorphisms of Levi degenerate hypersurfaces of finite multitype. By results of Kolar, Meylan, and Zaitsev in 2014, the Lie algebra of infinitesimal CR automorphisms may contain a graded component consisting of nonlinear vector fields of arbitrarily high degree, which has no analog in the classical Levi nondegenerate case, or in the case of finite type hypersurfaces in $\mathbb C^2$. We analyze this phenomenon for hypersurfaces of finite Catlin multitype with holomorphically nondegenerate models in complex dimension three. The results provide a complete classification of such manifolds. As a consequence, we show on which hypersurfaces 2-jets are not sufficient to determine an automorphism. The results also confirm a conjecture about the origin of nonlinear automorphisms of Levi degenerate hypersurfaces, formulated by the first author for an AIM workshop in 2010.References
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Bibliographic Information
- Martin Kolar
- Affiliation: Department of Mathematics and Statistics, Masaryk University, Kotlarska 2, 611 37 Brno, Czech Republic
- MR Author ID: 320160
- Email: mkolar@math.muni.cz
- Francine Meylan
- Affiliation: Department of Mathematics, University of Fribourg, CH 1700 Perolles, Fribourg, Switzerland
- MR Author ID: 355901
- Email: francine.meylan@unifr.ch
- Received by editor(s): August 10, 2015
- Received by editor(s) in revised form: January 11, 2016
- Published electronically: April 25, 2016
- Additional Notes: The first author was supported by the project CZ.1.07/2.3.00/20.0003 of the Operational Programme Education for Competitiveness of the Ministry of Education, Youth and Sports of the Czech Republic.
The second author was supported by Swiss NSF Grant 2100-063464.00/1 - Communicated by: Franc Forstneric
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 4807-4818
- MSC (2010): Primary 32V35, 32V40
- DOI: https://doi.org/10.1090/proc/13090
- MathSciNet review: 3544531