Kähler–Einstein metrics along the smooth continuity method

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 M...

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Published inGeometric and functional analysis Vol. 26; no. 4; pp. 975 - 1010
Main Authors Datar, Ved, Székelyhidi, Gábor
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.07.2016
Springer Nature B.V
Subjects
Analysis
Automorphisms
Manifolds
Mathematics
Mathematics and Statistics
Solitary waves
Solution strengthening
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Summary: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.
Bibliography:ObjectType-Article-1
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ISSN:1016-443X
1420-8970
DOI:10.1007/s00039-016-0377-4