Kähler–Einstein metrics on orbifolds and Einstein metrics on spheres

Abstract

A construction of Kähler–Einstein metrics using Galois coverings, studied by Arezzo–Ghigi–Pirola, is generalized to orbifolds. By applying it to certain orbifold covers of $C{P}^n$ which are trivial set theoretically, one obtains new Einstein metrics on odd-dimensional spheres. The method also gives Kähler–Einstein metrics on degree 2 Del Pezzo surfaces with $A_1$- or $A_2$-singularities.