Year: 2026
Type: preprint
Abstract: We prove the following two statements: (1) If $X$ is a compact Kähler fourfold with pseudo-effective canonical bundle and no subvarieties of codimension one or two, then $K_X$ is a torsion line bundle; (2) If $X$ is a compact Kähler fourfold with no subvarieties of codimension one or two, then $X$ is not uniruled. Using the Beauville-Bogomolov decomposition and a characterization of Uniruled manifolds by Wenhao Ou, we get that if $X$ is a compact Kähler fourfold with no subvarieties of codimension one or two, then either $X$ is a torus or an irreducible holomorphic symplectic manifold.
Source: arXiv (Cornell University)
Author: Vikash, Pisya
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7167642616