The α-invariant on toric fano manifolds

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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 languageEnglish (US)
Pages (from-to)1247-1259
Number of pages13
JournalAmerican Journal of Mathematics
Volume127
Issue number6
DOIs
StatePublished - Dec 2005
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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