Ohsawa-Takegoshi Extension Theorem for Compact Kähler Manifolds and Applications
Our main goal in this article is to prove an extension theorem for sections of the canonical bundle of a weakly pseudoconvex Kähler manifold with values in a line bundle endowed with a possibly singular metric. We also give some applications of our result.
KeywordsKähler manifolds Ohsawa-Takegoshi extension Singular metric
I would like to thank H. Tsuji who brought me attention to this problem during the Hayama conference 2013. I would also like to thank M. Păun for pointing out several interesting applications, and a serious mistake in the first version of the article. I would also like to thank J.-P. Demailly and X. Zhou for helpful discussions. Last but not least, I would like to thank the anonymous referee for excellent suggestions about this work.
- 1.B. Berndtsson, Integral formulas and the Ohsawa-Takegoshi extension theorem. Sci. China Ser. A 48(Suppl.), 61–73 (2005)Google Scholar
- 4.B. Berndtsson, M. Păun, Bergman kernels and subadjunction. arXiv: 1002.4145v1Google Scholar
- 5.J. Bertin, J.-P. Demailly, L. Illusie, C. Peters, Introduction to Hodge Theory. SMF/AMS Texts and Monographs, vol. 8 (2002)Google Scholar
- 7.B.-Y. Chen, A simple proof of the Ohsawa-Takegoshi extension theorem. ArXiv e-prints 1105.2430Google Scholar
- 8.J.-P. Demailly, Multiplier ideal sheaves and analytic methods in algebraic geometry, in School on Vanishing Theorems and Effective Results in Algebraic Geometry (Trieste, 2000). ICTP Lecture Notes, vol. 6 (ICTP, Trieste, 2001), pp. 1–148Google Scholar
- 9.J.-P. Demailly, Analytic Methods in Algebraic Geometry. Surveys of Modern Mathematics, vol. 1 (International Press, Boston, 2012)Google Scholar
- 10.J.-P. Demailly, Extension of holomorphic functions defined on non reduced analytic subvarieties. arXiv:1510.05230v1. Advanced Lectures in Mathematics Volume 35.1, the legacy of Bernhard Riemann after one hundred and fifty years, 2015Google Scholar
- 13.Q. Guan, X. Zhou, A solution of L 2 extension problem with optimal estimate and applications. Ann. Math. 181(3), 1139–1208 (2015). arXiv:1310.7169Google Scholar
- 15.P.H. Hiêp, The weighted log canonical threshold. C.R. Math. 352(4), 283–288 (2014)Google Scholar
- 20.Y.-T. Siu, Extension of twisted pluricanonical sections with plurisubharmonic weight and invariance of semipositively twisted plurigenera for manifolds not necessarily of general type, in Complex Geometry: Collection of Papers Dedicated to Hans Grauert (Springer, Berlin, 2002), pp. 223–277MATHGoogle Scholar
- 21.H. Tsuji, Extension of log pluricanonical forms from subvarieties. arXiv 0709.2710Google Scholar