Constructions of Kähler-Einstein metrics with negative scalar curvature

Jian Song; Ben Weinkove

doi:10.1007/s00208-009-0427-4

Constructions of Kähler-Einstein metrics with negative scalar curvature

Jian Song, Ben Weinkove

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

We show that on Kähler manifolds with negative first Chern class, the sequence of algebraic metrics introduced by Tsuji converges uniformly to the Kähler-Einstein metric. For algebraic surfaces of general type and orbifolds with isolated singularities, we prove a convergence result for a modified version of Tsuji's iterative construction.

Original language	English (US)
Pages (from-to)	59-79
Number of pages	21
Journal	Mathematische Annalen
Volume	347
Issue number	1
DOIs	https://doi.org/10.1007/s00208-009-0427-4
State	Published - Feb 2010
Externally published	Yes

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1007/s00208-009-0427-4

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title = "Constructions of K{\"a}hler-Einstein metrics with negative scalar curvature",

abstract = "We show that on K{\"a}hler manifolds with negative first Chern class, the sequence of algebraic metrics introduced by Tsuji converges uniformly to the K{\"a}hler-Einstein metric. For algebraic surfaces of general type and orbifolds with isolated singularities, we prove a convergence result for a modified version of Tsuji's iterative construction.",

author = "Jian Song and Ben Weinkove",

note = "Funding Information: J. Song is on leave for the semester and is visiting MSRI, Berkeley, CA as a postdoctoral fellow. He is supported in part by National Science Foundation grant DMS 0604805. Part of this research was carried out while B. Weinkove was a short-term visitor at MSRI in January 2007. He is supported in part by National Science Foundation grant DMS 0504285.",

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doi = "10.1007/s00208-009-0427-4",

language = "English (US)",

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journal = "Mathematische Annalen",

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AU - Song, Jian

AU - Weinkove, Ben

N1 - Funding Information: J. Song is on leave for the semester and is visiting MSRI, Berkeley, CA as a postdoctoral fellow. He is supported in part by National Science Foundation grant DMS 0604805. Part of this research was carried out while B. Weinkove was a short-term visitor at MSRI in January 2007. He is supported in part by National Science Foundation grant DMS 0504285.

PY - 2010/2

Y1 - 2010/2

N2 - We show that on Kähler manifolds with negative first Chern class, the sequence of algebraic metrics introduced by Tsuji converges uniformly to the Kähler-Einstein metric. For algebraic surfaces of general type and orbifolds with isolated singularities, we prove a convergence result for a modified version of Tsuji's iterative construction.

AB - We show that on Kähler manifolds with negative first Chern class, the sequence of algebraic metrics introduced by Tsuji converges uniformly to the Kähler-Einstein metric. For algebraic surfaces of general type and orbifolds with isolated singularities, we prove a convergence result for a modified version of Tsuji's iterative construction.

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ER -

Constructions of Kähler-Einstein metrics with negative scalar curvature

Abstract

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