On the limit behavior of metrics in the continuity method for the Kähler–Einstein problem on a toric Fano manifold
2012 ◽
Vol 148
(6)
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pp. 1985-2003
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Keyword(s):
AbstractThis 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.
2010 ◽
Vol 147
(1)
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pp. 319-331
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Keyword(s):
2019 ◽
Vol 2019
(757)
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pp. 1-50
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2011 ◽
Vol 226
(6)
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pp. 4921-4932
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2017 ◽
Vol 28
(04)
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pp. 1750024
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Keyword(s):
2015 ◽
Vol 2015
(703)
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2018 ◽
Vol 51
(1)
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pp. 34-42
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1987 ◽
Vol 39
(3)
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pp. 329-339
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