Kähler-Einstein metrics with cone singularities on klt pairs

2012/12/06 by Henri Guenancia, Guenancia, Henri
Mathematics · #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #math.CV #math.DG

paper · pdf · doi:10.48550/arxiv.1212.1383

19 pages

arxiv created 2012/12/06 · arxiv updated 2012/12/07

Abstract

Let (X,D) be a klt pair. Assuming either K_X+D big or -(K_X+D) ample, and that the coefficients of D are greater than 1/2, we show that the Kähler-Einstein metric attached to (X,D) -whenever it exists- has cone singularities along D on the log-smooth locus of the pair intersected with the ample locus of K_X+D (in the negatively curved case).

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