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Numerical Kodaira Dimension

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Birational Geometry of Foliations

Part of the book series: IMPA Monographs ((IMPA,volume 1))

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Abstract

In this chapter we study, following [30] , the first properties of the Zariski decomposition of the cotangent bundle of a nonrational foliation. In particular, we shall give a detailed description of the negative part of that Zariski decomposition, and we shall obtain a detailed classification of foliations whose Zariski decomposition is reduced to its negative part (i.e. foliations of numerical Kodaira dimension 0). We shall also discuss the “singular” point of view adopted in [30].

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References

  1. W. Barth, C. Peters, A. Van de Ven, Compact Complex Surfaces (Springer, Heidelberg, 1984)

    Book  MATH  Google Scholar 

  2. M. Brunella, Minimal models of foliated algebraic surfaces. Bull. SMF 127, 289–305 (1999)

    MATH  MathSciNet  Google Scholar 

  3. J.-P. Demailly, Regularization of closed positive currents and intersection theory. J. Algebraic Geom. 1, 361–409 (1992)

    MATH  MathSciNet  Google Scholar 

  4. T. Fujita, On Zariski problem. Proc. Japan Acad. Ser. A Math. Sci. no. 3, 106–110 (1979)

    Google Scholar 

  5. A. Lins Neto, Some examples for the Poincaré and Poincaré problems. Ann. Sci. École Norm. Sup. (4), no.2, 35, 231–266 (2002)

    Google Scholar 

  6. M. McQuillan, Noncommutative Mori Theory. Preprint IHES M/00/15 (2000)

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  7. Y. Miyaoka, T. Peternell, Geometry of Higher Dimensional Algebraic Varieties (Birkhäuser, Basel, 1997)

    Book  MATH  Google Scholar 

  8. F. Serrano, Fibred surfaces ad moduli. Duke Math. J. 67, 407–421 (1992)

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Authors and Affiliations

  1. Institut de Mathématiques de Bourgogne, UMR 5584 - CNRS Université de Bourgogne, Dijon, France

    Marco Brunella

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  1. Marco Brunella
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Brunella, M. (2015). Numerical Kodaira Dimension. In: Birational Geometry of Foliations. IMPA Monographs, vol 1. Springer, Cham. https://doi.org/10.1007/978-3-319-14310-1_8

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