Morrison-Kawamata cone conjecture for hyperkahler manifolds

By Ekaterina Amerik, Misha Verbitsky. 2014

53 citations recorded by the source corpus.

Let $M$ be a simple holomorphically symplectic manifold, that is, a simply connected holomorphically symplectic manifold of Kahler type with $h^{2,0}=1$. We prove that the group of holomorphic automorphisms of $M$ acts on the set of faces of its Kahler cone with finitely many orbits, whenever $b_2(M)\neq 5$. This is a version of the Morrison-Kawamata cone conjecture for hyperkahler manifolds. The proof is based on the following observation, proven with ergodic theory. Let $M$ be a complete Riemannian orbifold of dimension at least three, constant negative curvature and finite volume, and $\{S_i\}$ an infinite set of locally geodesic hypersurfaces. Then the union of $S_i$ is dense in $M$.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/6d7f46291101951e7f844806f25cc1915fa84dc2

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In Applied Mathematics

1. D. Huybrechts
2. Kieran G. O’Grady
3. E. Markman
4. Justin Sawon
5. A. Rapagnetta
6. Misha Verbitsky

In Geometry and Topology

1. D. Huybrechts
2. E. Markman
3. Kieran G. O’Grady
4. P. Stellari
5. Emanuele Macrì
6. Keiji Oguiso
7. Ulrike Riess
8. Justin Sawon

Citations in the corpus

• Lectures on K3 Surfaces (2016, background): “The cone conjecture for deformations of Hilb(X) with X a K3 surface has recently been established by Markman and Yoshioka in [388] and in general by Amerik and Verbitsky in [4].”