The $α$-Invariant on $CP^2#2\bar{CP^2}$

Jian Song

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The $α$-Invariant on $CP^2#2\bar{CP^2}$

Jian Song

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Abstract

In this paper, we apply the Tian-Yau-Zelditch expansion of the Bergman kernel on polarized Kähler metrics to approximate plurisubharmonic functions and compute the $α$-invariant of $CP^2#2\bar{CP^2}$, which is exactly 1/3. In addition we prove Tian's conjecture on the generalized Moser-Trudinger inequality in a special case prescribed by the $α$-invariant.

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BibTeX RIS

Jian Song. 2002-05-06. The $α$-Invariant on $CP^2#2\bar{CP^2}$. https://arxiv.org/abs/math/0205041

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