Work

Cones of Noether–Lefschetz divisors and moduli spaces of hyperkähler manifolds

Year: 2026

Type: article

Abstract: We give a general formula for generators of the NL cone on an orthogonal modular variety. This is the cone of effective divisors linearly equivalent to an effective linear combination of irreducible components of Noether–Lefschetz divisors. We apply this to describe, in terms of minimal generators, the NL cone of various moduli spaces of geometric origin such as those of polarized K3 surfaces, cubic fourfolds, and hyperkähler manifolds. Additionally, we establish uniruledness for many moduli spaces of primitively polarized hyperkähler manifolds of $${\textrm{OG6}}$$ OG6 and $${\textrm{Kum}}_n$$ Kum n -type. Finally, in analogy with the case of K3 surfaces of degree 2, we show that any family of polarized $${\textrm{Kum}}_2$$ Kum 2 -type hyperkähler manifolds with divisibility 2 and polarization degree 2 over a projective base is isotrivial.

Source: Mathematische Annalen

DOI: 10.1007/s00208-026-03372-1

Authors: Ignacio Barros, Pietro Beri, Laure Flapan, Brandon Williams

Institutions: University of Antwerp, Institut Élie Cartan de Lorraine, Michigan State University, Heidelberg University

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190