Injectivity theorem for pseudo-effective line bundles and its applications
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- by Osamu Fujino and Shin-ichi Matsumura;
- Trans. Amer. Math. Soc. Ser. B 8 (2021), 849-884
- DOI: https://doi.org/10.1090/btran/86
- Published electronically: October 13, 2021
- HTML | PDF
Abstract:
We formulate and establish a generalization of Kollár’s injectivity theorem for adjoint bundles twisted by suitable multiplier ideal sheaves. As applications, we generalize Kollár’s torsion-freeness, Kollár’s vanishing theorem, and a generic vanishing theorem for pseudo-effective line bundles. Our approach is not Hodge theoretic but analytic, which enables us to treat singular Hermitian metrics with nonalgebraic singularities. For the proof of the main injectivity theorem, we use $L^{2}$-harmonic forms on noncompact Kähler manifolds. For applications, we prove a Bertini-type theorem on the restriction of multiplier ideal sheaves to general members of free linear systems.References
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Bibliographic Information
- Osamu Fujino
- Affiliation: Department of Mathematics, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
- MR Author ID: 652921
- Email: fujino@math.kyoto-u.ac.jp
- Shin-ichi Matsumura
- Affiliation: Mathematical Institute, Tohoku University, 6-3, Aramaki Aza-Aoba, Aoba-ku, Sendai 980-8578, Japan.
- MR Author ID: 1006398
- ORCID: 0000-0002-5928-527X
- Email: mshinichi-math@tohoku.ac.jp, mshinichi0@gmail.com
- Received by editor(s): May 7, 2019
- Received by editor(s) in revised form: June 15, 2021, and June 25, 2021
- Published electronically: October 13, 2021
- Additional Notes: The first author was partially supported by Grant-in-Aid for Young Scientists (A) 24684002 from JSPS and by JSPS KAKENHI Grant Numbers JP16H03925, JP16H06337, JP19H01787, JP20H00111, JP21H00974. The second author was partially supported by Grand-in-Aid for Young Scientists (A) $\sharp$17H04821, Grand-in-Aid for Scientific Research (B) $\sharp$ 21H00976, and Fostering Joint International Research (A) $\sharp$ 19KK0342 from JSPS
- © Copyright 2021 by the authors under Creative Commons Attribution-Noncommercial 3.0 License (CC BY NC 3.0)
- Journal: Trans. Amer. Math. Soc. Ser. B 8 (2021), 849-884
- MSC (2020): Primary 32L10; Secondary 32Q15
- DOI: https://doi.org/10.1090/btran/86
- MathSciNet review: 4324359
Dedicated: Dedicated to Professor Ichiro Enoki on the occasion of his retirement