On an injectivity theorem for log-canonical pairs with analytic adjoint ideal sheaves
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 K\"ahler 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 K\"ahler 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.
Keywords
Cite
@article{arxiv.2205.06954,
title = {On an injectivity theorem for log-canonical pairs with analytic adjoint ideal sheaves},
author = {Tsz On Mario Chan and Young-Jun Choi},
journal= {arXiv preprint arXiv:2205.06954},
year = {2023}
}
Comments
43 pages; v2: presentations in Remark 2.4.3 and proofs of Propositions 3.3.2 and 3.3.4 are expanded; accepted for publication in the Trans. Amer. Math. Soc