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Extension theorems, non-vanishing and the existence of good minimal models

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Acta Mathematica

Abstract

We prove an extension theorem for effective purely log-terminal pairs (X, S + B) of non-negative Kodaira dimension \({\kappa (K_X+S+B)\ge 0}\) . The main new ingredient is a refinement of the Ohsawa–Takegoshi L 2 extension theorem involving singular Hermitian metrics.

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Authors and Affiliations

  1. Département de Mathématiques, Institut Fourier, Université de Grenoble I, FR-38402, Saint-Martin d’Hères, France

    Jean-Pierre Demailly

  2. Department of Mathematics, University of Utah, 155 South 1400 East JWB 233, Salt Lake City, UT, 84112, U.S.A.

    Christopher D. Hacon

  3. Institut Élie Cartan, Université Henri Poincaré, B. P. 70239, FR-54506, Vandoeuvre-lès-Nancy Cedex, France

    Mihai Păun

Authors
  1. Jean-Pierre Demailly
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  2. Christopher D. Hacon
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  3. Mihai Păun
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Correspondence to Mihai Păun.

Additional information

The second author was partially supported by NSF research grant no. 0757897. During an important part of the preparation of this article, the third author was visiting KIAS (Seoul); he wishes to express his gratitude for the support and excellent working conditions provided by this institute. We would like to thank F. Ambro, B. Berndtsson, Y. Gongyo and C. Xu for interesting conversations about this article.

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Demailly, JP., Hacon, C.D. & Păun, M. Extension theorems, non-vanishing and the existence of good minimal models. Acta Math 210, 203–259 (2013). https://doi.org/10.1007/s11511-013-0094-x

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  • DOI: https://doi.org/10.1007/s11511-013-0094-x

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