Singular set of some Kähler orbifolds

Jeffres, Thalia

doi:10.1090/S0002-9947-97-01796-0

Singular set of some Kähler orbifolds
HTML articles powered by AMS MathViewer

by Thalia D. Jeffres PDF

Trans. Amer. Math. Soc. 349 (1997), 1961-1971 Request permission

Abstract:

We consider some examples of orbifolds with positive first Chern class. Applying a result of Ding and Tian, we show that the singularities must be very mild if the orbifold admits a Kähler-Einstein metric.

References

D. Bättig and H. Knörrer, “Singularitäten”, Birkhäuser, 1991.
W. Barth, C. Peters, and A. Van de Ven, Compact complex surfaces, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 4, Springer-Verlag, Berlin, 1984. MR 749574, DOI 10.1007/978-3-642-96754-2
Wei Yue Ding and Gang Tian, Kähler-Einstein metrics and the generalized Futaki invariant, Invent. Math. 110 (1992), no. 2, 315–335. MR 1185586, DOI 10.1007/BF01231335
Akito Futaki, Kähler-Einstein metrics and integral invariants, Lecture Notes in Mathematics, vol. 1314, Springer-Verlag, Berlin, 1988. MR 947341, DOI 10.1007/BFb0078084
Toshiki Mabuchi and Shigeru Mukai, Stability and Einstein-Kähler metric of a quartic del Pezzo surface, Einstein metrics and Yang-Mills connections (Sanda, 1990) Lecture Notes in Pure and Appl. Math., vol. 145, Dekker, New York, 1993, pp. 133–160. MR 1215285
G. Tian, On Calabi’s conjecture for complex surfaces with positive first Chern class, Invent. Math. 101 (1990), no. 1, 101–172. MR 1055713, DOI 10.1007/BF01231499