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Fibers of the Baum-Bott map for foliations of degree two on ℙ2

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Abstract

The Baum-Bott map associates to a foliation the Baum-Bott indexes of their singularities. In this paper we study the fibers of the Baum-Bott map in the space of foliations of degree two on the projective plane ℙ2. In the main result we prove that its generic fiber contains exactly 240 orbits of the natural action of Aut(ℙ2) onthespace of foliations.

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References

  1. M. Brunella. Birational geometry of foliations; text book for a course in the First Latin American Congress of Mathematics, IMPA (2000).

  2. A. Campillo and J. Olivares. A plane foliation of degree different from 1 is determined by its singular scheme. C.R. Acad. Sci. Paris Sér. I Math., 328(10) (1999), 877–882.

    MathSciNet  MATH  Google Scholar 

  3. C. Camacho and P. Sad. Invariant varieties through singularities of holomorphic vector fields. Ann. of Math., 115 (1982), 579–595.

    Article  MathSciNet  MATH  Google Scholar 

  4. A. Guillot. Semicompletness of homogeneous quadratic vector fields. Ann. Inst. Fourier (Grenoble), 56 (2006), 1583–1615.

    Article  MathSciNet  MATH  Google Scholar 

  5. J.P. Jouanolou. équations de Pfaff algèbriques. Lecture Notes in Math., 708, Springer-Verlag, Berlin (1979).

    MATH  Google Scholar 

  6. A. Lins Neto. Algebraic solutions of polynomial differential equations and foliations in dimension two. Lect. Notes in Math., 1345, 192–231.

  7. A. Lins Neto. Some examples for the Poincaré and Painlevé problems. Ann. Scientifiques de l’école Norm. Sup., 4eme série, t. 35, pg. 231–266 (2002).

    Article  MathSciNet  MATH  Google Scholar 

  8. A. Lins Neto. Curvature of pencils of foliations. Analyse complexe, systèmes dynamiques, sommabilité des séries divergentes et théories galoisiennes. I. Astérisque, 296 (2004), 167–190.

    MathSciNet  Google Scholar 

  9. A. Lins Neto and J.V. Pereira. The generic rank of the Baum-Bott map for foliations of the projective plane. Compos. Math., 142(6) (2006), 1549–1586.

    Article  MathSciNet  MATH  Google Scholar 

  10. B. Azevedo Scárdua. Transversely affine and transversely projective holomorphic foliations. Ann. Sci. école Norm. Sup., (4) 30(2) (1997), 169–204.

    MATH  Google Scholar 

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Authors and Affiliations

  1. Instituto de Matemática Pura e Aplicada, Estrada Dona Castorina, 110, Horto, Rio de Janeiro, Brasil

    Alcides Lins Neto

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  1. Alcides Lins Neto
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Correspondence to Alcides Lins Neto.

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Dedicated to Jean-François Mattei in his 60th birthday

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Neto, A.L. Fibers of the Baum-Bott map for foliations of degree two on ℙ2 . Bull Braz Math Soc, New Series 43, 129–169 (2012). https://doi.org/10.1007/s00574-012-0008-0

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  • DOI: https://doi.org/10.1007/s00574-012-0008-0

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