On the cone conjecture for Enriques manifolds
Algebraic Geometry
2026-05-27 v3
Abstract
Enriques manifolds are non--simply connected manifolds whose universal cover is irreducible holomorphic symplectic, and as such they are natural generalizations of Enriques surfaces. The goal of this note is to prove the Morrison--Kawamata cone conjecture for very general Enriques manifolds when the degree of the cover is prime. The proof uses the analogous result (established by Amerik--Verbitsky) for their universal cover. We also verify the conjecture for a very general Enriques manifold which is deformation equivalent to one of the known examples.
Cite
@article{arxiv.2303.07095,
title = {On the cone conjecture for Enriques manifolds},
author = {Gianluca Pacienza and Alessandra Sarti},
journal= {arXiv preprint arXiv:2303.07095},
year = {2026}
}