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arXiv · 2504.01753

Well-clipped cones under finite quotients and applications to the cone conjecture

Cécile Gachet
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Abstract

We introduce a property of convex cones, being "well-clipped", that is inspired by the work of several complex algebraic geometers on the Morrison-Kawamata cone conjecture. That property is satisfied by movable cones of divisors on various complex projective varieties of Calabi-Yau type, such as abelian varieties and projective hyperkähler manifolds. The property of being well-clipped has the advantage to descend under taking invariants by a finite group action, and to be stable under direct sums. In the class of well-clipped cones, we also provide a simple characterization of those cones that admit a rational polyhedral fundamental domain under some natural group action. We use this framework to prove the movable cone conjecture for finite quotients of various projective varieties of Calabi-Yau type, notably products of projective primitive symplectic varieties, abelian varieties, and smooth rational surfaces underlying klt Calabi-Yau pairs. This entails Enriques manifolds in the sense of Oguiso-Schröer. We also provide Galois descent statements implying the movable Morrison-Kawamata cone conjecture for abelian varieties over arbitrary perfect fields.

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Cécile Gachet. 2026-05-13. Well-clipped cones under finite quotients and applications to the cone conjecture. https://arxiv.org/abs/2504.01753

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