A complete normal form for everywhere Levi degenerate hypersurfaces in $\mathbb C^{3}$
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2019
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| _version_ | 1866913661276127232 |
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| author | Kolar, Martin Kossovskiy, Ilya |
| author_facet | Kolar, Martin Kossovskiy, Ilya |
| contents | $2$-nondegenerate real hypersurfaces in complex manifolds play an important role in CR-geometry and the theory of Hermitian Symmetric Domains. In this paper, we construct a complete convergent normal form for everywhere $2$-nondegenerate real-analytic hypersurfaces in complex $3$-space. We do so by developing the homological approach of Chern-Moser in the $2$-nondegenerate setting. This seems to be the first such construction for hypersurfaces of infinite Catlin multitype. Our approach is based on using a rational (nonpolynomial) model for everywhere $2$-nondegenerate hypersurfaces, which is the local realization due to Fels-Kaup of the well known tube over the light cone.
As an application, we obtain, in the spirit of Chern-Moser theory, a criterion for the local sphericity (i.e. local equivalence to the model) for a $2$-nondegenerate hypersurface in terms of its normal form. As another application, we obtain an explicit description of the moduli space of everywhere $2$-nondegenerate hypersurfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1905_05629 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | A complete normal form for everywhere Levi degenerate hypersurfaces in $\mathbb C^{3}$ Kolar, Martin Kossovskiy, Ilya Complex Variables $2$-nondegenerate real hypersurfaces in complex manifolds play an important role in CR-geometry and the theory of Hermitian Symmetric Domains. In this paper, we construct a complete convergent normal form for everywhere $2$-nondegenerate real-analytic hypersurfaces in complex $3$-space. We do so by developing the homological approach of Chern-Moser in the $2$-nondegenerate setting. This seems to be the first such construction for hypersurfaces of infinite Catlin multitype. Our approach is based on using a rational (nonpolynomial) model for everywhere $2$-nondegenerate hypersurfaces, which is the local realization due to Fels-Kaup of the well known tube over the light cone. As an application, we obtain, in the spirit of Chern-Moser theory, a criterion for the local sphericity (i.e. local equivalence to the model) for a $2$-nondegenerate hypersurface in terms of its normal form. As another application, we obtain an explicit description of the moduli space of everywhere $2$-nondegenerate hypersurfaces. |
| title | A complete normal form for everywhere Levi degenerate hypersurfaces in $\mathbb C^{3}$ |
| topic | Complex Variables |
| url | https://arxiv.org/abs/1905.05629 |