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Constructions of Kähler–Einstein metrics with negative scalar curvature

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Abstract

We show that on Kähler manifolds with negative first Chern class, the sequence of algebraic metrics introduced by Tsuji converges uniformly to the Kähler–Einstein metric. For algebraic surfaces of general type and orbifolds with isolated singularities, we prove a convergence result for a modified version of Tsuji’s iterative construction.

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Authors and Affiliations

  1. Department of Mathematics, Johns Hopkins University, Baltimore, MD, 21218, USA

    Jian Song

  2. Department of Mathematics, Harvard University, Cambridge, MA, 02138, USA

    Ben Weinkove

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  1. Jian Song
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  2. Ben Weinkove
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Correspondence to Jian Song.

Additional information

J. Song is on leave for the semester and is visiting MSRI, Berkeley, CA as a postdoctoral fellow. He is supported in part by National Science Foundation grant DMS 0604805. Part of this research was carried out while B. Weinkove was a short-term visitor at MSRI in January 2007. He is supported in part by National Science Foundation grant DMS 0504285.

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Song, J., Weinkove, B. Constructions of Kähler–Einstein metrics with negative scalar curvature. Math. Ann. 347, 59–79 (2010). https://doi.org/10.1007/s00208-009-0427-4

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  • DOI: https://doi.org/10.1007/s00208-009-0427-4

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