The α-invariant on toric fano manifolds

Jian Song

doi:10.1353/ajm.2005.0043

The α-invariant on toric fano manifolds

Jian Song

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

22 Scopus citations

Abstract

The global holomorphic α-invariant plays an important role in the study of the existence of Kähler-Einstein metrics on complex manifolds with positive first Chern class. In this paper, we apply the Tian-Yau-Zelditch expansion of the Szegö kernel on polarized Kahler metrics to approximate almost plurisubharmonic functions and derive a formula to compute the α-invariant on toric Fano manifolds.

Original language	English (US)
Pages (from-to)	1247-1259
Number of pages	13
Journal	American Journal of Mathematics
Volume	127
Issue number	6
DOIs	https://doi.org/10.1353/ajm.2005.0043
State	Published - Dec 2005
Externally published	Yes

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1353/ajm.2005.0043

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abstract = "The global holomorphic α-invariant plays an important role in the study of the existence of K{\"a}hler-Einstein metrics on complex manifolds with positive first Chern class. In this paper, we apply the Tian-Yau-Zelditch expansion of the Szeg{\"o} kernel on polarized Kahler metrics to approximate almost plurisubharmonic functions and derive a formula to compute the α-invariant on toric Fano manifolds.",

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AB - The global holomorphic α-invariant plays an important role in the study of the existence of Kähler-Einstein metrics on complex manifolds with positive first Chern class. In this paper, we apply the Tian-Yau-Zelditch expansion of the Szegö kernel on polarized Kahler metrics to approximate almost plurisubharmonic functions and derive a formula to compute the α-invariant on toric Fano manifolds.

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The α-invariant on toric fano manifolds

Abstract

All Science Journal Classification (ASJC) codes

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