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 ℂℙn 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 A1- or A2-singularities.
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Alessandro Ghigi, János Kollár, Kähler-Einstein metrics on orbifolds and Einstein metrics on spheres. Comment. Math. Helv. 82 (2007), no. 4, pp. 877–902DOI 10.4171/CMH/113