The $\alpha $-invariant on certain surfaces with symmetry groups

Jian Song
2004 Transactions of the American Mathematical Society  
The global holomorphic α-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 α-invariant on CP 2 #nCP 2 for n = 1, 2, 3.
doi:10.1090/s0002-9947-04-03484-1 fatcat:dwtgaexl5nc4lisqwbdhb5plae