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

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.

Cite this article

Alessandro Ghigi, János Kollár, Kähler-Einstein metrics on orbifolds and Einstein metrics on spheres. Comment. Math. Helv. 82 (2007), no. 4, pp. 877–902

DOI 10.4171/CMH/113