JournalscmhVol. 82 , No. 4DOI 10.4171/cmh/113

Kähler-Einstein metrics on orbifolds and Einstein metrics on spheres

  • Alessandro Ghigi

    Università degli Studi di Milano-Bicocca, Italy
  • János Kollár

    Fine Hall / Princeton University, USA
Kähler-Einstein metrics on orbifolds and Einstein metrics on spheres cover

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 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.