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On Fano Foliations 2

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Foliation Theory in Algebraic Geometry

Part of the book series: Simons Symposia ((SISY))

Abstract

In this paper we pursue the study of mildly singular del Pezzo foliations on complex projective manifolds started in [AD13].

An erratum to this chapter can be found at 10.1007/978-3-319-24460-0_8

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References

  1. Araujo C, Druel S (2013) On Fano foliations. Adv Math 238:70–118

    Article  MathSciNet  MATH  Google Scholar 

  2. Araujo C, Druel S (2014) On codimension 1 del Pezzo foliations on varieties with mild singularities. Math Ann 360(3–4):769–798

    Article  MathSciNet  MATH  Google Scholar 

  3. Araujo C, Druel S, Kovács SJ (2008) Cohomological characterizations of projective spaces and hyperquadrics. Invent Math 174(2):233–253

    Article  MathSciNet  MATH  Google Scholar 

  4. Bosch S, Lütkebohmert W, Raynaud M (1995) Formal and rigid geometry. IV. The reduced fibre theorem. Invent Math 119(2):361–398

    Article  MATH  Google Scholar 

  5. Brunella M (2004) Birational geometry of foliations. IMPA Mathematical Publications, Instituto de Matemática Pura e Aplicada (IMPA), Rio de Janeiro

    Google Scholar 

  6. Campana F, Koziarz V, Păun M (2012) Numerical character of the effectivity of adjoint line bundles. Ann Inst Fourier (Grenoble) 62(1):107–119

    Article  MathSciNet  MATH  Google Scholar 

  7. Déserti J, Cerveau D (2006) Feuilletages et actions de groupes sur les espaces projectifs. Mém Soc Math Fr (NS) (2005) 103:vi+124 p

    Google Scholar 

  8. Demailly J-P (1997) Algebraic criteria for Kobayashi hyperbolic projective varieties and jet differentials. Algebraic geometry—Santa Cruz 1995. Proc. Symp. Pure Math., vol 62. Am. Math. Soc., Providence, pp 285–360

    Google Scholar 

  9. Fujita T (1975) On the structure of polarized varieties with \(\Delta\)-genera zero. J Fac Sci Univ Tokyo Sect IA Math 22:103–115

    MathSciNet  MATH  Google Scholar 

  10. Fujita T (1980) On the structure of polarized manifolds with total deficiency one. I. J Math Soc Jpn 32(4):709–725

    Article  MathSciNet  MATH  Google Scholar 

  11. Fujita T (1982) On polarized varieties of small \(\Delta\)-genera. Tohoku Math J (2) 34(3): 319–341

    Article  MathSciNet  MATH  Google Scholar 

  12. Fujino O (2011) Fundamental theorems for the log minimal model program. Publ Res Inst Math Sci 47(3):727–789

    Article  MathSciNet  MATH  Google Scholar 

  13. Höring A (2014) Twisted cotangent sheaves and a kobayashi-ochiai theorem for foliations. Ann Inst Fourier (Grenoble) 64(6):2465–2480

    Article  MathSciNet  MATH  Google Scholar 

  14. Kawakita M (2007) Inversion of adjunction on log canonicity. Invent Math 167(1): 129–133

    Article  MathSciNet  MATH  Google Scholar 

  15. Kollár J, Mori S (1998) Birational geometry of algebraic varieties. Cambridge Tracts in Mathematics, vol 134. Cambridge University Press, Cambridge. With the collaboration of C. H. Clemens and A. Corti, Translated from the 1998 Japanese original

    Google Scholar 

  16. Kobayashi S, Ochiai T (1973) Characterizations of complex projective spaces and hyperquadrics. J Math Kyoto Univ 13:31–47

    MathSciNet  MATH  Google Scholar 

  17. Kollár J (1996) Rational curves on algebraic varieties. Ergebnisse der Mathematik und ihrer Grenzgebiete, vol 32. Springer, Berlin

    Book  Google Scholar 

  18. Kollár J (1997) Singularities of pairs. Algebraic geometry—Santa Cruz 1995. Proc. Symp. Pure Math., vol 62. Am. Math. Soc., Providence, pp 221–287

    Google Scholar 

  19. Kollár J (2013) Singularities of the minimal model program. Cambridge Tracts in Mathematics, vol 200. Cambridge University Press, Cambridge. With a collaboration of Sándor Kovács

    Google Scholar 

  20. Loray F, Pereira JV, Touzet F (2013) Foliations with trivial canonical bundle on Fano 3-folds. Math Nachr 286(8–9):921–940

    Article  MathSciNet  MATH  Google Scholar 

  21. McQuillan M (2008) Canonical models of foliations. Pure Appl Math Q 4(3, part 2):877–1012

    Google Scholar 

  22. Nakayama N (2007) Classification of log del Pezzo surfaces of index two. J Math Sci Univ Tokyo 14(3):293–498

    MathSciNet  MATH  Google Scholar 

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Acknowledgements

Much of this work was developed during the authors’ visits to IMPA and Institut Fourier. We would like to thank both institutions for their support and hospitality. The first named author was partially supported by CNPq and Faperj Research Fellowships. The second named author was partially supported by the CLASS project of the A.N.R.

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Authors and Affiliations

  1. IMPA, Estrada Dona Castorina 110, Rio de Janeiro, 22460-320, Brazil

    Carolina Araujo

  2. Institut Fourier, UMR 5582 du CNRS, Université Grenoble 1, BP 74, 38402, Saint Martin d’Hères, France

    Stéphane Druel

Authors
  1. Carolina Araujo
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  2. Stéphane Druel
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Corresponding author

Correspondence to Carolina Araujo .

Editor information

Editors and Affiliations

  1. Mathematics Department, Imperial College of London, London, UK

    Paolo Cascini

  2. Department of Mathematics, UC San Diego, La Jolla, CA, USA

    James McKernan

  3. IMPA, Rio de Janeiro, Brazil

    Jorge Vitório Pereira

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Araujo, C., Druel, S. (2016). On Fano Foliations 2. In: Cascini, P., McKernan, J., Pereira, J.V. (eds) Foliation Theory in Algebraic Geometry. Simons Symposia. Springer, Cham. https://doi.org/10.1007/978-3-319-24460-0_1

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