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The Kähler cone of a hyperkähler manifold. (Le cône kählérien d’une variété hyperkählérienne.) (French) Zbl 1068.32014
Summary: We answer a question of D. Huybrechts about the Kähler cone of a compact hyper-Kähler manifold. More precisely, we show how the methods he uses to describe the closure of this cone do in fact extend to get the following description: the Kähler cone of a hyper-Kähler manifold is the set of elements of the positive cone attached to the canonical quadratic form which are positive on the rational curves.

MSC:
32J27 Compact Kähler manifolds: generalizations, classification
53C26 Hyper-Kähler and quaternionic Kähler geometry, “special” geometry
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