Kähler-Einstein metrics on orbifolds and Einstein metrics on spheres

Alessandro Ghigi; János Kollár

doi:10.4171/CMH/113

Kähler-Einstein metrics on orbifolds and Einstein metrics on spheres

Alessandro Ghigi, János Kollár

Mathematics

Research output: Contribution to journal › Article › peer-review

29 Scopus citations

Abstract

A construction of Kähler-Einstein metrics using Galois coverings, studied by ArezzoGhigi-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.

Original language	English (US)
Pages (from-to)	877-902
Number of pages	26
Journal	Commentarii Mathematici Helvetici
Volume	82
Issue number	4
DOIs	https://doi.org/10.4171/CMH/113
State	Published - 2007

All Science Journal Classification (ASJC) codes

General Mathematics

Keywords

Einstein metrics
Exotic spheres
Kähler-Einstein orbifolds
Sasakian manifolds

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10.4171/CMH/113

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AU - Kollár, János

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AB - A construction of Kähler-Einstein metrics using Galois coverings, studied by ArezzoGhigi-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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KW - Exotic spheres

KW - Kähler-Einstein orbifolds

KW - Sasakian manifolds

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Kähler-Einstein metrics on orbifolds and Einstein metrics on spheres

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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