Year: 2026
Type: preprint
Abstract: We consider smooth proper families of compact complex manifolds over a disk whose total space is Kähler, together with a boundary divisor with relative simple normal crossings. We prove that, if the boundary is a rational divisor with coefficients in $[0,1)$, every logarithmic pluricanonical form on a fiber extends to a neighborhood of that fiber, and hence that the logarithmic plurigenera are constant. No positivity of the log canonical class is assumed. We prove further that, for real boundary coefficients in $[0,1]$, a log-adjoint class twisted by a smooth semipositive form has the same volume on every fiber, and that it is pseudoeffective either on every fiber or on none. When the log-adjoint class is nef on every fiber, we give a second proof of the extension theorem, which does not use the minimal model program.
Source: arXiv (Cornell University)
Authors: Liu, Kefeng, Wan, Xueyuan
Institution: Chongqing University of Technology
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G2775328943, G504305494, G5374330193
OpenAlex ID: W7223041585