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A general extension theorem for cohomology classes on non reduced analytic subspaces

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Abstract

The main purpose of this paper is to generalize the celebrated L 2 extension theorem of Ohsawa and Takegoshi in several directions: The holomorphic sections to extend are taken in a possibly singular hermitian line bundle, the subvariety from which the extension is performed may be non reduced, the ambient manifold is Kähler and holomorphically convex, but not necessarily compact.

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Acknowledgements

This work was supported by the Agence Nationale de la Recherche grant “Convergence de Gromov-Hausdorff en géométrie kählérienne ”, the European Research Council project “Algebraic and Kähler Geometry” (Grant No. 670846) from September 2015, the Japan Society for the Promotion of Science Grant-in-Aid for Young Scientists (B) (Grant No. 25800051) and the Japan Society for the Promotion of Science Program for Advancing Strategic International Networks to Accelerate the Circulation of Talented Researchers.

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Authors and Affiliations

  1. Institut de Mathématiques de Jussieu, Université Pierre et Marie Curie, Paris, 75252, France

    JunYan Cao

  2. Institut Fourier, Université Grenoble Alpes, Gières, 38610, France

    Jean-Pierre Demailly

  3. Mathematical Institute, Tohoku University, Sendai, 980-8578, Japan

    Shin-ichi Matsumura

Authors
  1. JunYan Cao
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  2. Jean-Pierre Demailly
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  3. Shin-ichi Matsumura
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Correspondence to Jean-Pierre Demailly.

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In memory of Professor LU QiKeng (1927–2015)

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Cao, J., Demailly, JP. & Matsumura, Si. A general extension theorem for cohomology classes on non reduced analytic subspaces. Sci. China Math. 60, 949–962 (2017). https://doi.org/10.1007/s11425-017-9066-0

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  • DOI: https://doi.org/10.1007/s11425-017-9066-0

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