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The Kähler Ricci flow on Fano manifolds (I)

Xiuxiong ChenBing Wang — 2012

Journal of the European Mathematical Society

We study the evolution of pluri-anticanonical line bundles K M - ν along the Kähler Ricci flow on a Fano manifold M . Under some special conditions, we show that the convergence of this flow is determined by the properties of the pluri-anticanonical divisors of M . For example, the Kähler Ricci flow on M converges when M is a Fano surface satisfying c 1 2 ( M ) = 1 or c 1 2 ( M ) = 3 . Combined with the works in [CW1] and [CW2], this gives a Ricci flow proof of the Calabi conjecture on Fano surfaces with reductive automorphism groups....

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