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March 2021 Boundary behavior of Kähler-Einstein metric of negative ricci curvature over quasi-projective manifolds with boundary of general type
Shin Kikuta
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Kodai Math. J. 44(1): 81-114 (March 2021). DOI: 10.2996/kmj44106

Abstract

In this paper, we discuss an asymptotic boundary behavior of the complete Kähler-Einstein metric of negative Ricci curvature on a quasi-projective manifold with semiample log-canonical bundle. In particular, we focus our attention on its relations with degeneration of positivity for the log-canonical bundle on the boundary divisor. Based on a pioneering result due to G. Schumacher, a fundamental conjecture about the relations is proposed in this paper. Moreover it is also proved that the conjecture actually holds in the case when the boundary divisor is of general type.

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Shin Kikuta. "Boundary behavior of Kähler-Einstein metric of negative ricci curvature over quasi-projective manifolds with boundary of general type." Kodai Math. J. 44 (1) 81 - 114, March 2021. https://doi.org/10.2996/kmj44106

Information

Received: 19 March 2020; Published: March 2021
First available in Project Euclid: 23 March 2021

Digital Object Identifier: 10.2996/kmj44106

Subjects:
Primary: 32Q20
Secondary: 32W20 , 53C21 , 53C44

Keywords: (almost-)complete Kähler-Einstein metric of negative Ricci curvature , asymptotic boundary behavior , Kähler-Ricci flow , singular Kähler-Einstein metric

Rights: Copyright © 2021 Tokyo Institute of Technology, Department of Mathematics

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Vol.44 • No. 1 • March 2021
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