Year: 2026
Type: preprint
Abstract: We give a geometric proof of the following statement: let $X$ be a smooth hyperkähler fourfold such that the Picard group is generated by a line bundle $L$ that is nef, non-trivial, and not big. If the Kodaira dimension of $L$ is non-negative, some positive multiple defines a Lagrangian fibration. The proof requires a number of tools which are of independent interest, including an analogue of Voisin's unobstructedness result and a smoothing result for singular Lagrangian subvarieties.
Source: arXiv (Cornell University)
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223355124