Asymptotics of complete Kähler-Einstein metrics -- negativity of the holomorphic sectional curvature
type: Item
instance of: scholarly article
title: Asymptotics of complete Kähler-Einstein metrics -- negativity of the holomorphic sectional curvature
zbMATH Open document ID: 1022.32008
author: Georg Schumacher
published in: Documenta Mathematica
publication date: 2003-10-21T00:00:00Z
full work available at URL: https://eudml.org/doc/50350
full work available at URL: 20.html
review text: Complete Kähler-Einstein metrics \(ds_{X}^{2}\) of constant Ricci curvature on quasiprojective varieties are of interest in various geometric situations. Theorem 1. Let \(\overline{X}\) be a compact complex surface, \(C \subset \overline{X}\) a smooth divisor satisfying the condition \[ K_{\overline{X}} + C > 0. \] Then the holomorphic sectional curvature of the complete Kähler-Einstein metric on \(X = \overline{X}\mathbb C\) is bounded from above by a negative constant near the compactifying divisor. The sectional and holomorphic bisectional curvature are bounded on \(X.\) Theorem 2. The Kähler-Einstein metric \(\omega_{X}\) converges to the Kähler-Einstein metric \(\omega_{C},\) when restricted to directions parallel to \(C.\)
reviewed by: V. V. Chueshev
Mathematics Subject Classification ID: 32Q05
Mathematics Subject Classification ID: 32Q20
Mathematics Subject Classification ID: 53C55
zbMATH DE Number: 1862905
zbMATH Keywords: complete Kähler-Einstein metrics of constant Ricci curvature on quasiprojective varieties
zbMATH Keywords: holomorphic sectional curvature
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1862905