Geodesic
Pluricomplex Green's functions and Fano manifolds
Épijournal de Géométrie Algébrique, Tome 3 (2019)

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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. 
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     author = {McCleerey, Nicholas and Tosatti, Valentino},
     title = {Pluricomplex {Green's} functions and {Fano} manifolds},
     journal = {\'Epijournal de G\'eom\'etrie Alg\'ebrique},
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     volume = {3},
     year = {2019},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/epiga.2019.volume3.4706/}
}
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McCleerey, Nicholas; Tosatti, Valentino. Pluricomplex Green's functions and Fano manifolds. Épijournal de Géométrie Algébrique, Tome 3 (2019). doi: 10.46298/epiga.2019.volume3.4706

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