Le cône kählérien d'une variété hyperkählérienne

Abstract

We answer a question of D. Huybrechts about the Kähler cone of a compact hyperkähler 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 hyperkähler manifold is the set of elements of the positive cone attached to the canonical quadratic form which are positive on the rational curves.