Tsz On Mario Chan

collaborators

5 papers

math.CV2026

An extension theorem in terms of adjoint ideal sheaves

Tsz On Mario Chan

In the context of the study of the Ohsawa--Takegoshi $L^{2}$ extension theorem, a "qualitative" extension theorem in terms of adjoint ideal sheaves (i.e. extension result without $L^…

math.AG2024

A solution to Fujita's freeness conjecture via an extension theorem with analytic adjoint ideal sheaves

Tsz On Mario Chan

The effective freeness in Fujita's conjecture states that, for an ample line bundle $L$ on a complex projective manifold $X$ , the adjoint bundle $K_{X} \otimes L^{\otimes m}$ is globa…

math.CV2024

An application of adjoint ideal sheaves to injectivity and extension theorems

Tsz On Mario Chan, Young-Jun Choi

This note reviews the authors' approach to Fujino's conjecture, i.e. the injectivity theorem for lc pairs on compact KÃ¤hler manifolds, via the use of adjoint ideal sheaves coupled…

math.CV2024

Injectivity theorems for higher direct images under proper KÃ¤hler morphisms on snc spaces

Tsz On Mario Chan, Young-Jun Choi, Shin-ichi Matsumura

Let $X$ be a complex manifold, and let $Y$ and $D$ be two reduced simple-normal-crossing (snc) divisors on $X$ with no common irreducible components. Given a proper locally KÃ¤hler…

math.CV2024

An injectivity theorem on snc compact KÃ¤hler spaces: an application of the theory of harmonic integrals on log-canonical centers via adjoint ideal sheaves

Tsz On Mario Chan, Young-Jun Choi, Shin-ichi Matsumura

Let $(X, D)$ be a log-canonical (lc) pair, in which $X$ is a compact KÃ¤hler manifold and $D$ is a reduced snc divisor, and let $F$ be a holomorphic line bundle on $X$ equipped with…