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Complex Analysis and Geometry pp 119–133Cite as

Structure Theorems for Compact Kähler Manifolds with Nef Anticanonical Bundles

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 144))

Abstract

This survey presents various results concerning the geometry of compact Kähler manifolds with numerically effective first Chern class: structure of the Albanese morphism of such manifolds, relations tying semipositivity of the Ricci curvature with rational connectedness, positivity properties of the Harder-Narasimhan filtration of the tangent bundle.

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Notes

  1. 1.

    Added in proof. In a very recent manuscript, Takayuki Koike has established the existence of such nef and non semipositive configurations, cf. arXiv:1507.00109, “Ueda theory for compact curves with nodes”.

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Authors and Affiliations

  1. Institut Fourier, Université de Grenoble I, BP74, 100 rue des Maths, 38402, Saint-Martin d’Hères, France

    Jean-Pierre Demailly

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  1. Jean-Pierre Demailly
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Correspondence to Jean-Pierre Demailly .

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Editors and Affiliations

  1. Department of Mathematics, Università di Roma Tor Vergata, Rome, Italy

    Filippo Bracci

  2. Dept. of Mathematics Education, Kyungnam University, Changwon, Korea (Republic of)

    Jisoo Byun

  3. Université Joseph Fourier Grenoble, Institut Fourier, Grenoble, France

    Hervé Gaussier

  4. Graduate School of Mathematical Sciences, The University of Tokyo, Meguro-ku, Tokyo, Japan

    Kengo Hirachi

  5. Department of Mathematics, POSTECH, Pohang, Korea (Republic of)

    Kang-Tae Kim

  6. Department of Mathematics, Bergische Universität Wuppertal, Wuppertal, Nordrhein-Westfalen, Germany

    Nikolay Shcherbina

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Demailly, JP. (2015). Structure Theorems for Compact Kähler Manifolds with Nef Anticanonical Bundles. In: Bracci, F., Byun, J., Gaussier, H., Hirachi, K., Kim, KT., Shcherbina, N. (eds) Complex Analysis and Geometry. Springer Proceedings in Mathematics & Statistics, vol 144. Springer, Tokyo. https://doi.org/10.1007/978-4-431-55744-9_8

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