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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63979In 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.16 pagesDifferential GeometryThe $α$-Invariant on $CP^2#2\bar{CP^2}$text