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Real Submanifolds of \(\mathbf{C}^2\) With Singularities

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Abstract

We consider real submanifolds of \(\mathbf{C}^2\) with singularities of three types: \(RC\)-singular 2 - dimensional surfaces, real quadratic cones, and hypersurfaces with degeneration of the Levi form. The holomorphic automorphisms of singular germs are evaluated. We also discuss resolution of singularities in the context of \(\mathit{CR}\) geometry.

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Acknowledgments

The author is grateful to A.V. Domrin and I.G. Kossovskiy for their discussion of the this topic.

Funding

This work was supported by the Russian Science Foundation (grant no. 23-21-00109), https://rscf.ru/project/23-21-00109/.

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Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia

    V. K. Beloshapka

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  1. V. K. Beloshapka
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Correspondence to V. K. Beloshapka.

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Beloshapka, V.K. Real Submanifolds of \(\mathbf{C}^2\) With Singularities. Russ. J. Math. Phys. 30, 280–293 (2023). https://doi.org/10.1134/S1061920823030020

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  • DOI: https://doi.org/10.1134/S1061920823030020

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