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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