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

Mathematische Annalen volume 366, pages 101–120 (2016)Cite this article

Abstract

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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Authors and Affiliations

  1. Department of Mathematics, Stony Brook University, Stony Brook, NY, 11794-3651, USA

    Henri Guenancia

  2. Department of Mathematics, University of Connecticut, 196 Auditorium Road, Storrs, CT, 06269-3009, USA

    Damin Wu

Authors
  1. Henri Guenancia
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  2. Damin Wu
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Corresponding author

Correspondence to Henri Guenancia.

Additional information

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). https://doi.org/10.1007/s00208-015-1306-9

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  • DOI: https://doi.org/10.1007/s00208-015-1306-9

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