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A Poincaré type inequality for one-dimensional multiprojective foliations

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Abstract

We study one-dimensional holomorphic foliations on products of complex projective spaces and present results giving the number of singularities, counting multiplicities, of a generic foliation, a criterion for a foliation to be Riccati and a Poincaré type inequality, relating degrees of foliations to degrees of hypersurfaces which are invariant by them.

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Author information

Authors and Affiliations

  1. Departamento de Matemática — UFV, Av. PH. Rolfs s/n, 36571-000, Viçsa, MG, Brazil

    Maurício Corrêa Jr.

  2. Departamento de Matemática — UFMG, Av. Antonio Carlos, 6627, 31270-901, Belo Horizonte, MG, Brazil

    Márcio G. Soares

Authors
  1. Maurício Corrêa Jr.
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  2. Márcio G. Soares
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Corresponding author

Correspondence to Maurício Corrêa Jr..

Additional information

This work was partially supported by CNPq and CAPES-Brasil.

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Corrêa, M., Soares, M.G. A Poincaré type inequality for one-dimensional multiprojective foliations. Bull Braz Math Soc, New Series 42, 485–503 (2011). https://doi.org/10.1007/s00574-011-0026-3

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  • DOI: https://doi.org/10.1007/s00574-011-0026-3

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