Kähler--Einstein metrics on quasi-projective manifolds

2023/09/07 by Dang, Quang-Tuan, Vu, Duc-Viet · 1 citation
#32Q15 #32U15 #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2309.03858

Abstract

Let X be a compact Kähler manifold and D be a simple normal crossing divisor on X such that K_X+D is big and nef. We first prove that the singular Kähler--Einstein metric constructed by Berman--Guenancia is almost-complete on X \backslash D in the sense of Tian--Yau. In our second main result, we establish the weak convergence of conic Kähler--Einstein metrics of negative curvature to the above-mentioned metric when K_X+D is merely big, answering partly a recent question posed by Biquard--Guenancia. Potentials of low energy play an important role in our approach.

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