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Remarks on the Symmetries of a Model Hypersurface

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Abstract

In this partly expository paper, we deal with sharp jet determination results following from a generalization of the Chern—Moser theory to Levi degenerate hypersurfaces with polynomial models, as obtained in [30]. We formulate the jet determination results for finitely smooth hypersurfaces of finite type. Another goal of the paper is to gain more understanding of the symmetries for such hypersurfaces, which violate 2-jet determination. Finally, we collect and state some open problems regarding the existence of graded components of strictly positive weight of the Lie Algebra of symmetries for the model hypersurface

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Acknowledgement

The authors would like to thank the referee for his very careful reading and for having enriched this paper with several important remarks and useful references.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Masaryk University, Kotlarska 2, 611 37, Brno, Czech Republic

    M. Kolář

  2. Department of Mathematics, University of Fribourg, CH 1700, Perolles, Fribourg, Switzerland

    F. Meylan

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  1. M. Kolář
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  2. F. Meylan
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Correspondence to F. Meylan.

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To László Lempert for his 70th birthday

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Kolář, M., Meylan, F. Remarks on the Symmetries of a Model Hypersurface. Anal Math 48, 545–565 (2022). https://doi.org/10.1007/s10476-022-0157-3

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  • DOI: https://doi.org/10.1007/s10476-022-0157-3

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