Work

Some density results for hyperkähler manifolds

Year: 2025

Type: article

Abstract: Lagrangian fibrations of hyperkähler manifolds are induced by semi-ample line bundles which are isotropic with respect to the Beauville-Bogomolov-Fujiki form. For a non-isotrivial family of hyperkähler manifolds over a complex manifold $S$ of positive dimension, we prove that the set of points in $S$, for which there is an isotropic class in the Picard lattice of the corresponding hyperkähler manifold represented as a fiber over that point, is analytically dense in $S$. We also prove the expected openness and density of the locus of polarised hyperkähler manifolds that admit a nef algebraic isotropic line bundle.

Source: Mathematical Research Letters

DOI: 10.4310/mrl.251214175204

Authors: Yajnaseni Dutta, Elham Izadi, Ljudmila Kamenova, Lisa Marquand

Institutions: Leiden University, University of California San Diego, Stony Brook University, Courant Institute of Mathematical Sciences, New York University

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Simons Foundation Autism Research Initiative

Award: G7604153415