Nicholas McCleerey ; Valentino Tosatti - Pluricomplex Green's functions and Fano manifolds

epiga:4706 - Épijournal de Géométrie Algébrique, June 21, 2019, Volume 3 - https://doi.org/10.46298/epiga.2019.volume3.4706
Pluricomplex Green's functions and Fano manifoldsArticle

Authors: Nicholas McCleerey ; Valentino Tosatti

    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.


    Volume: Volume 3
    Published on: June 21, 2019
    Accepted on: May 30, 2019
    Submitted on: July 23, 2018
    Keywords: Mathematics - Complex Variables,32W20, 32U35, 14J45, 32Q20, 53C25
    Funding:
      Source : OpenAIRE Graph
    • RTG: Analysis on Manifolds; Funder: National Science Foundation; Code: 1502632

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