The geometry of Kähler cones

Abstract

The Kähler cone of a compact manifold carries a natural Riemannian metric, given by the intersection product of its cohomology ring. We write down the curvature tensor of this metric by embedding the Kähler cone in the space of hermitian metrics on the underlying manifold. After discussing weak functorality and completeness properties, we give a relative version of both the Kähler cone and the metric.

13 pages

Cited by in corpus (1)

• A flat Higgs bundle structure on the complexified Kähler cone