On an injectivity theorem for log-canonical pairs with analytic adjoint ideal sheaves
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- by Tsz On Mario Chan and Young-Jun Choi;
- Trans. Amer. Math. Soc. 376 (2023), 8337-8381
- DOI: https://doi.org/10.1090/tran/8935
- Published electronically: September 14, 2023
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Abstract:
As an application of the residue functions corresponding to the lc-measures developed by the authors, the proof of the injectivity theorem on compact Kähler manifolds for plt pairs by Matsumura is improved in this article to allow multiplier ideal sheaves of plurisubharmonic functions with neat analytic singularities in the coefficients of the relevant cohomology groups. With the use of a refined version of analytic adjoint ideal sheaves, a plan towards a solution to the generalised version of Fujino’s conjecture (i.e. an injectivity theorem on compact Kähler manifolds for lc pairs with multiplier ideal sheaves) is laid down and, in addition to the result for plt pairs, a proof for lc pairs in dimension $2$, which is also an improvement of Matsumura’s result, is given.References
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Bibliographic Information
- Tsz On Mario Chan
- Affiliation: Dept. of Mathematics, Pusan National University, Busan 46241, South Korea
- MR Author ID: 1028897
- ORCID: 0000-0001-7252-6499
- Email: mariochan@pusan.ac.kr
- Young-Jun Choi
- Affiliation: Dept. of Mathematics, Pusan National University, Busan 46241, South Korea
- MR Author ID: 880466
- ORCID: 0000-0003-3838-8568
- Email: youngjun.choi@pusan.ac.kr
- Received by editor(s): August 31, 2022
- Received by editor(s) in revised form: February 11, 2023
- Published electronically: September 14, 2023
- Additional Notes: This work was supported by the National Research Foundation (NRF) of Korea grant funded by the Korea government (No. 2018R1C1B3005963 and No. 2023R1A2C1007227).
- © Copyright 2023 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 376 (2023), 8337-8381
- MSC (2020): Primary 32J25; Secondary 32Q15, 14B05
- DOI: https://doi.org/10.1090/tran/8935
- MathSciNet review: 4669299
Dedicated: In the memory of Prof. Jean-Pierre Demailly