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Article Dans Une Revue Mathematische Annalen Année : 2016

On the boundary behavior of Kähler–Einstein metrics on log canonical pairs

Résumé

In this paper, we study the boundary behavior of the negatively curved Kähler-Einstein metric attached to a log canonical pair (X, D) such that K X + D is ample. In the case where X is smooth and D has simple normal crossings support (but possibly negative coefficients), we provide a very precise estimate on the potential of the KE metric near the boundary D. In the more general singular case (D being assumed effective though), we show that the KE metric has mixed cone and cusp singularities near D on the snc locus of the pair. As a corollary, we derive the behavior in codimension one of the KE metric of a stable variety.
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Dates et versions

hal-01878994 , version 1 (18-11-2020)

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Damin Wu, Henri Guenancia. On the boundary behavior of Kähler–Einstein metrics on log canonical pairs. Mathematische Annalen, 2016, 366 (1-2), pp.101 - 120. ⟨10.1007/s00208-015-1306-9⟩. ⟨hal-01878994⟩
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