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arXiv · 2303.07095

On the cone conjecture for Enriques manifolds

Gianluca Pacienza·Alessandra Sarti
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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.

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Gianluca Pacienza, Alessandra Sarti. 2023-03-13. On the cone conjecture for Enriques manifolds. https://doi.org/10.46298/epiga.2026.11097

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