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Kähler-Einstein metrics for some quasi-smooth log del Pezzo surfaces

Author(s): Carolina Araujo
Journal: Trans. Amer. Math. Soc. 354 (2002), 4303-4312.
MSC (2000): Primary 14Q10, 32Q20
Posted: July 2, 2002
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Abstract: Recently Johnson and Kollár determined the complete list of anticanonically embedded quasi-smooth log del Pezzo surfaces in weighted projective $3$-spaces. They also proved that many of those surfaces admit a Kähler-Einstein metric, and that some of them do not have tigers.

The aim of this paper is to settle the question of the existence of Kähler-Einstein metrics and tigers for those surfaces for which the question was left open. In order to do so, we will use techniques developed earlier by Nadel, Demailly and Kollár.

References:

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C. P. Boyer, K. Galicki and M. Nakamaye: On the Geometry of Sasakian-Einstein 5-manifolds. Preprint DG/0012047 (2001).

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J.-P. Demailly and J. Kollár: Semi-continuity of complex singularity exponents and Kähler-Einstein metrics on Fano orbifolds. Preprint AG/9910118 (1999), Ann. Scient. École Norm. Sup. Paris 34 (2001), 525-556. MR 2002e:32032

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Additional Information:

Carolina Araujo
Affiliation: Mathematics Department, Princeton University, Princeton, New Jersey 08544
Email: caraujo@math.princeton.edu

DOI: 10.1090/S0002-9947-02-03081-7
PII: S 0002-9947(02)03081-7
Received by editor(s): December 12, 2001
Posted: July 2, 2002
Additional Notes: Partial financial support was provided by CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico - Brazil)
Copyright of article: Copyright 2002, American Mathematical Society

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