Year: 2023
Type: preprint
Abstract: Let $X$ be a compact Kähler manifold whose anticanonical cohomology class is semipositive. Let $L$ be a big and semi-ample line bundle on $X$ and $α$ be the Chern class of $L$. We give a sufficient condition ensuring that the solution of the complex Monge-Ampère equations in $α$ with $L^p$ right-hand side ($p>1$) is $\log^M$-continuous for every constant $M>0$. As an application, we show that every singular Ricci-flat metric in a semi-ample integral class in a projective Calabi-Yau surface $X$ is globally $\log^M$-continuous with respect to a smooth metric on $X$.
Source: arXiv (Cornell University)
Authors: Do, Hoang-Son, Vu, Duc-Viet
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4389501117