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3 results for “Morrison-Kawamata”

Collections of parabolic orbits in homogeneous spaces, homogeneous dynamics and hyperkahler geometrymath.AG

Study improves cone conjecture on hyperkahler manifolds using homogeneous space dynamics.

problem Improving the Morrison-Kawamata cone conjecture on hyperkahler manifolds.

method Ergodic theory on homogeneous spaces.

result Beauville-Bogomolov square of MBM classes is bounded by a number depending only on the manifold's deformation class.

hyperkahler geometry cone conjecture ergodic theory homogeneous spaces Morrison-Kawamata

2016-04-13abs ↗pdf ↗

Morrison-Kawamata cone conjecture for hyperkahler manifoldsmath.AG

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 …

2014-08-18abs ↗pdf ↗

Hyperbolic geometry of the ample cone of a hyperkahler manifoldmath.AG

Hyperbolic geometry on ample cone of hyperkahler manifolds.

problem Understanding the ample cone structure of hyperkahler manifolds via hyperbolic geometry.

method Analyzing the Bogomolov-Beauville-Fujiki quadratic form and its restriction to the rational Hodge lattice, leading to a hyperbolic orbifold.

result Existence of finitely many geodesic hypersurfaces cutting the orbifold into polyhedral pieces, each isometric to a quotient of the ample cone of a birational model.

hyperkahler manifolds ample cone hyperbolic geometry Bogomolov-Beauville-Fujiki form orbifold

2015-11-07abs ↗pdf ↗