Acta Mathematica

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

Jean-Pierre Demailly, Christopher D. Hacon, and Mihai Păun

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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 L2 extension theorem involving singular Hermitian metrics.


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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Acta Math., Volume 210, Number 2 (2013), 203-259.

Received: 23 February 2011
Revised: 4 November 2012
First available in Project Euclid: 31 January 2017

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2013 © Institut Mittag-Leffler


Demailly, Jean-Pierre; Hacon, Christopher D.; Păun, Mihai. Extension theorems, non-vanishing and the existence of good minimal models. Acta Math. 210 (2013), no. 2, 203--259. doi:10.1007/s11511-013-0094-x.

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