A numerical characterization of ball quotients for normal surfaces with branch loci. (English) Zbl 0704.53053
The authors show that Kähler-Einstein geometry fits in with the theory of minimal models for normal surfaces with branch loci. From this they obtain an inequality of Miyaoka-Yau type for canonical normal surfaces with branch loci and with at worst log-canonical singularities and the equality characterizes ball quotients with finite volume. Details of this note can be found in F. Sakai’s survey paper [Algebraic geometry, Proc. Summer Res. Inst., Brunswick/Maine 1985, part 1, Proc. Symp. Pure Math. 46, 451-465 (1987; Zbl 0636.14013), M. Nakamura’s master thesis (Saitama University 1989), and R. Kobayashi’s article [Uniformization of complex surfaces (preprint)].
Reviewer: Gh.Pitiş
MSC:
| 53C55 | Global differential geometry of Hermitian and Kählerian manifolds |
| 32C20 | Normal analytic spaces |
Keywords:
Kähler-Einstein geometry; minimal models; normal surfaces; branch loci; log-canonical singularitiesCitations:
Zbl 0636.14013References:
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