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Existence of dicritical singularities of Levi-flat hypersurfaces and holomorphic foliations

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Abstract

We study holomorphic foliations tangent to singular real-analytic Levi-flat hypersurfaces in compact complex manifolds of complex dimension two. We give some hypotheses to guarantee the existence of dicritical singularities of these objects. As consequence, we give some applications to holomorphic foliations tangent to real-analytic Levi-flat hypersurfaces with singularities in \(\mathbb {P}^2\).

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Acknowledgements

The authors wishes to express his thanks to Alcides Lins Neto (IMPA) for several helpful comments during the preparation of the paper. Also, we would like to thank the referee for suggestions and pointing out corrections.

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Authors and Affiliations

  1. Dpto. Ciencias - Sección Matemáticas, Pontificia Universidad Católica del Perú, Av. Universitaria 1801, San Miguel, Lima 32, Peru

    Andrés Beltrán & Hernán Neciosup

  2. Departamento de Matemática - ICEX, Universidade Federal de Minas Gerais, UFMG, Av. Antônio Carlos 6627, Belo Horizonte, MG, 31270-901, Brazil

    Arturo Fernández-Pérez

Authors
  1. Andrés Beltrán
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  2. Arturo Fernández-Pérez
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  3. Hernán Neciosup
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Corresponding author

Correspondence to Arturo Fernández-Pérez.

Additional information

This work is supported by the Pontificia Universidad Católica del Perú Project VRI-DGI 2016-1-0018. Second author is partially supported by CNPq Grant Number 301825/2016-5.

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Beltrán, A., Fernández-Pérez, A. & Neciosup, H. Existence of dicritical singularities of Levi-flat hypersurfaces and holomorphic foliations. Geom Dedicata 196, 35–44 (2018). https://doi.org/10.1007/s10711-017-0303-4

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  • DOI: https://doi.org/10.1007/s10711-017-0303-4

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