Abstract
The purpose of this paper is to give two supplements for vanishing theorems: One is a relative version of the Kawamata-Viehweg-Nadel type vanishing theorem, which is obtained from an observation for the variation of the numerical dimension of singular hermitian line bundles. The other is an analytic injectivity theorem for log canonical pairs on surfaces, which can be seen as a partial answer for Fujino’s conjecture.
Dedicated to Professor Kang-Tae Kim on the occasion of his 60th birthday.
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Acknowledgements
This paper has been written during author’s stay in Institut de Mathématiques de Jussieu-Paris Rive gauche (IMJ-PRG). The author would like to thank the members of IMJ-PRG for their hospitality. He is supported by the Grant-in-Aid for Young Scientists (A) \(\sharp \)17H04821 from JSPS and the JSPS Program for Advancing Strategic International Networks to Accelerate the Circulation of Talented Researchers.
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Matsumura, Si. (2018). Variation of Numerical Dimension of Singular Hermitian Line Bundles. In: Byun, J., Cho, H., Kim, S., Lee, KH., Park, JD. (eds) Geometric Complex Analysis. Springer Proceedings in Mathematics & Statistics, vol 246. Springer, Singapore. https://doi.org/10.1007/978-981-13-1672-2_19
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