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VOL. 18.2 | 1990 Uniformization of Complex Surfaces

Abstract

This is an expository paper on the structure of complex surfaces which have the Hirzebruch proportionality $3c_2 = c_1^2$ or $2c_2 = c_1^2$ between their Chern numbers. We characterize surfaces with $3c_2 = c_1^2$ as ball quotients in the category of normal surfaces with branch loci. We discuss the uniformization problem for surfaces with $2c_2 = c_1^2$ from the point of view of Kähler–Einstein metrics and holomorphic conformal structures.

Information

Published: 1 January 1990
First available in Project Euclid: 17 June 2018

zbMATH: 0755.32024
MathSciNet: MR1145252

Digital Object Identifier: 10.2969/aspm/01820313

Rights: Copyright © 1990 Mathematical Society of Japan

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Vol. 18.2 • 1 January 1990
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