Abstract
We study the Fujita-type conjecture proposed by Popa and Schnell. We obtain an effective bound on the global generation of direct images of pluri-adjoint line bundles on the regular locus. We also obtain an effective bound on the generic global generation for a Kawamata log canonical \(\mathbb {Q}\)-pair. We use analytic methods such as \(L^2\) estimates, \(L^2\) extensions and injective theorems of cohomology groups.
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Acknowledgements
The author would like to thank his supervisor Prof. Shigeharu Takayama for helpful comments and enormous support. He wishes to thank Genki Hosono for several useful discussions. He also wishes to thank Yajnaseni Dutta for letting him know their results in [8] and sending their preprint. He is greatly indebted to the referee for many kind advices. This work is supported by the Program for Leading Graduate Schools, MEXT, Japan. This work is also supported by JSPS KAKENHI Grant Number 17J04457.
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Iwai, M. On the global generation of direct images of pluri-adjoint line bundles. Math. Z. 294, 201–208 (2020). https://doi.org/10.1007/s00209-019-02266-0
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DOI: https://doi.org/10.1007/s00209-019-02266-0