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A Comprehensive Approach to the Moduli Space of Quasi-homogeneous Singularities

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Singularities and Foliations. Geometry, Topology and Applications (NBMS 2015, BMMS 2015)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 222))

Abstract

We study the relationship between singular holomorphic foliations at \((\mathbb {C}^{2},0)\) and their separatrices. Under mild conditions we describe a complete set of analytic invariants characterizing foliations with quasi-homogeneous separatrices. Further, we give the full moduli space of quasi-homogeneous plane curves. This paper has an expository character in order to make it accessible also to non-specialists.

This work was partially supported by CAPES-PROCAD grant no. 0007056.

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Author information

Authors and Affiliations

  1. Departamento de Matemática, Universidade Federal do Espírito Santo, Av. Fernando Ferrari 514, Vitória-ES, 29075-910, Brazil

    Leonardo M. Câmara

  2. Intituto de Matemática, Universidade Federal do Rio de Janeiro, Caixa Postal 68530, Rio de Janeiro-RJ, 21945-970, Brazil

    Bruno Scárdua

Authors
  1. Leonardo M. Câmara
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  2. Bruno Scárdua
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Corresponding author

Correspondence to Leonardo M. Câmara .

Editor information

Editors and Affiliations

  1. ICMC, University of São Paulo, São Carlos, São Paulo, Brazil

    Raimundo Nonato Araújo dos Santos

  2. Department of Mathematics, Federal University of Paraíba, João Pessoa, Paraíba, Brazil

    Aurélio Menegon Neto

  3. Mathematics Institute, University of Warwick, Coventry, United Kingdom

    David Mond

  4. ICMC, University of São Paulo, São Carlos, São Paulo, Brazil

    Marcelo J. Saia

  5. Instituto de Matemáticas, Unidad Cuernavaca, Universidad Nacional Autónoma de México, Cuernavaca, Morelos, Mexico

    Jawad Snoussi

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Câmara, L.M., Scárdua, B. (2018). A Comprehensive Approach to the Moduli Space of Quasi-homogeneous Singularities. In: Araújo dos Santos, R., Menegon Neto, A., Mond, D., Saia, M., Snoussi, J. (eds) Singularities and Foliations. Geometry, Topology and Applications. NBMS BMMS 2015 2015. Springer Proceedings in Mathematics & Statistics, vol 222. Springer, Cham. https://doi.org/10.1007/978-3-319-73639-6_15

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