Pluricomplex Green's functions and Fano manifolds

Abstract

We show that if a Fano manifold does not admit Kahler-Einstein metrics then the Kahler potentials along the continuity method subconverge to a function with analytic singularities along a subvariety which solves the homogeneous complex Monge-Ampere equation on its complement, confirming an expectation of Tian-Yau.

Keywords

• mathematics - complex variables
• 32w20, 32u35, 14j45, 32q20, 53c25