English

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

Differential Geometry 2007-05-23 v1

Abstract

In this paper, we apply the Tian-Yau-Zelditch expansion of the Bergman kernel on polarized K\"ahler metrics to approximate plurisubharmonic functions and compute the α\alpha-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\alpha-invariant.

Cite

@article{arxiv.math/0205041,
  title  = {The $\alpha$-Invariant on $CP^2#2\bar{CP^2}$},
  author = {Jian Song},
  journal= {arXiv preprint arXiv:math/0205041},
  year   = {2007}
}

Comments

16 pages

R2 v1 2026-07-22T16:45:07.021Z