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New Irreducible Components of the Space of Foliations Associated to the Affine Lie Algebra

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Abstract

We construct a family of irreducible components of space of holomorphic foliations of codimension one on \(\mathbb {P}^3\) associated to some affine Lie algebra.

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References

  • Artal, E., Martín-Morales, J., Ortigas-Galindo, J.: Intersection theory on abelian-quotient V-surfaces and Q-resolutions. J. Singul. 8, 11–30 (2014)

    MathSciNet  MATH  Google Scholar 

  • Batyrev, V., Cox, D.: On the Hodge Structure of Projective Hypersurfaces in Toric Varieties. Duke Math. J. 75, 293–338 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  • Brunella, M.: Foliations on complex projective surfaces. Dynamical systems. Part II, 4977, Pubbl. Cent. Ric. Mat. Ennio Giorgi, Scuola Norm. Sup., Pisa (2003)

  • Calvo-Andrade, O.: Positivity, vanishing theorems and rigidity of Codimension one Holomorphic Foliations. Annnalles de la Faculté des Sciencies de Toulouse. 299, XVIII(4), 811–854 (2009)

  • Calvo-Andrade, O., Cerveau, D., Giraldo, L., Lins, A.: Neto. Irreducible components of the space of foliations associated to the affine Lie algebra. Ergodic Theory Dynam. Syst. 24(4), 987–1014 (2004)

    Article  MATH  Google Scholar 

  • Cerveau, D., Mattei, J.-F.: Formes intégrables holomorphes singuliéres. Astérique 97, SMF (1982)

  • Cerveau, D., Lins-Neto, A.: Irreducible components of the space of holomorphic foliations of degree two in \(\mathbb{P}^n\). Ann. Math. 143, 577–612 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  • Corrêa Jr., M., Soares, M.G.: A note on Poincaré problem for quasi-homogeneous foliations. Proc. Am. Math. Soc. 140(9), 3145–3150 (2012)

    Article  MATH  Google Scholar 

  • Cox, D.: The homogeneous coordinate ring of a toric variety. J. Algebraic Geom. 4, 17–50 (1995)

    MathSciNet  MATH  Google Scholar 

  • Cukierman, F., Pereira, J.V.: Stability of holomorphic foliations with split tangent sheaf. Am. J. Math. 130(2), 413–439 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  • Cukierman, F., Soares, M., Vainsencher, I.: Singularities of logarithmic foliations. Compos. Math. 142(1), 131–142 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  • Dolgachev, I.: Weighted projective varieties. In: Carrel, J.B. (ed.) Group Actions Fields. Lecture Notes in Math., vol. 956, pp. 34–71. Springer, Berlin (1982)

  • Griffiths, P., Harris, J.: Principles of algebraic geometry. Wiley Classics Library Edition Published (1994)

  • Jouanolou, J.P.: Equations de Pfaff algébriques. Lect. Notes Math., vol. 708. Springer (1979)

  • Loray, F., Pereira, J.V., Touzet, F.: Foliations with trivial canonical bundle on Fano 3-folds. Math. Nachr. 286(8–9), 921940.1522-2616 (2013)

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Acknowledgements

The author wish to express his thanks to Jorge Vitório Pereira for his help in the elaboration of this paper and to IMPA and UFJF where a great part of this paper has been written. This work was partially supported by CNPq and CAPES.

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Correspondence to Ruben Lizarbe.

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Lizarbe, R. New Irreducible Components of the Space of Foliations Associated to the Affine Lie Algebra. Bull Braz Math Soc, New Series 48, 377–388 (2017). https://doi.org/10.1007/s00574-017-0029-9

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  • DOI: https://doi.org/10.1007/s00574-017-0029-9

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