Pluricomplex green's functions and fano manifolds

Nicholas McCleerey, Valentino Tosatti

Research output: Contribution to journalArticlepeer-review

Abstract

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

Original languageEnglish (US)
Article numberY
JournalEpijournal de Geometrie Algebrique
Volume3
StatePublished - 2019

Keywords

  • Algebraic Kähler potentials
  • Fano manifold
  • Pluricomplex green function

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology

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