Kähler-Einstein metrics: from cones to cusps

2015/04/08 by Guenancia, Henri · 1 citation
#Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1504.01947

Abstract

In this note, we prove that on a compact Kähler manifold X carrying a smooth divisor D such that K_X+D is ample, the Kähler-Einstein cusp metric is the limit (in a strong sense) of the Kähler-Einstein conic metrics when the cone angle goes to 0. We further investigate the boundary behavior of those and prove that the rescaled metrics converge to a cylindrical metric on \mathbb C^*× \mathbb C^n-1.

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