Limits of conical Kähler-Einstein metrics on rank one horosymmetric spaces

Abstract

We consider families of conical Kähler-Einstein metrics on rank one horosymmetric Fano manifolds, with decreasing cone angles along a codimension one orbit. At the limit angle, which is positive, we show that the metrics, restricted to the complement of that orbit, converge to (the pull-back of) the Kähler-Einstein metric on the basis of the horosymmetric homogeneous space, which is a projective homogeneous space. Then we show that, on the symmetric space fibers, the rescaled metrics converge to Stenzel's Ricci flat Kähler metrics.

11 pages

References in corpus (1)

• Degenerating Kähler-Einstein cones, locally symmetric cusps, and the Tian-Yau metric