The 𝛼-invariant on certain surfaces with symmetry groups

Song, Jian

doi:10.1090/S0002-9947-04-03484-1

The $\alpha$-invariant on certain surfaces with symmetry groups
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by Jian Song PDF

Trans. Amer. Math. Soc. 357 (2005), 45-57 Request permission

Abstract:

The global holomorphic $\alpha$-invariant introduced by Tian is closely related to the existence of Kähler-Einstein metrics. We apply the result of Tian, Yau and Zelditch on polarized Kähler metrics to approximate plurisubharmonic functions and compute the $\alpha$-invariant on $CP^2\#n\overline {CP^2}$ for $n=1,2,3$.

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