The Kähler cone of a hyperkähler manifold. (Le cône kählérien d’une variété hyperkählérienne.) (French) Zbl 1068.32014

Boucksom, Sébastien

C. R. Acad. Sci., Paris, Sér. I, Math. 333, No. 10, 935-938 (2001).

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