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


In this paper, we study the boundary behavior of the negatively curved Kähler–Einstein metric attached to a log canonical pair (XD) 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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Correspondence to Henri Guenancia.

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Damin Wu was partially supported by the NSF Grant DMS-1308837.

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Guenancia, H., Wu, D. On the boundary behavior of Kähler–Einstein metrics on log canonical pairs . Math. Ann. 366, 101–120 (2016).

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