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  • On the limit behavior of metrics in the continuity method for the Kähler–Einstein problem on a toric Fano manifold

  • Part of
  • Chi Li
  • Journal:
    Compositio Mathematica / Volume 148 / Issue 6 / November 2012
    Published online by Cambridge University Press:
    12 October 2012, pp. 1985-2003
    Print publication:
    November 2012
    • Article
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  • This work is a continuation of the author’s previous paper [Greatest lower bounds on the Ricci curvature of toric Fano manifolds, Adv. Math. 226 (2011), 4921–4932]. On any toric Fano manifold, we discuss the behavior of the limit metric of a sequence of metrics which are solutions to a continuity family of complex Monge–Ampère equations in the Kähler–Einstein problem. We show that the limit metric satisfies a singular complex Monge–Ampère equation. This gives a conic-type singularity for the limit metric. Information on conic-type singularities can be read off from the geometry of the moment polytope.