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Kähler–Einstein metrics along the smooth continuity method

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Abstract

We show that if a Fano manifold M is K-stable with respect to special degenerations equivariant under a compact group of automorphisms, then M admits a Kähler–Einstein metric. This is a strengthening of the solution of the Yau–Tian–Donaldson conjecture for Fano manifolds by Chen–Donaldson–Sun (Int Math Res Not (8):2119–2125, 2014), and can be used to obtain new examples of Kähler–Einstein manifolds. We also give analogous results for twisted Kähler–Einstein metrics and Kahler–Ricci solitons.

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Authors and Affiliations

  1. Department of Mathematics, University of California, Berkeley, CA, 94720, USA

    Ved Datar

  2. Department of Mathematics, University of Notre Dame, 255 Hurley, Notre Dame, IN, 46556, USA

    Gábor Székelyhidi

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  1. Ved Datar
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  2. Gábor Székelyhidi
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Datar, V., Székelyhidi, G. Kähler–Einstein metrics along the smooth continuity method. Geom. Funct. Anal. 26, 975–1010 (2016). https://doi.org/10.1007/s00039-016-0377-4

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