Kähler Ricci flow on Fano manifolds(I)

2009/09/13 by Chen, Xiuxiong, Wang, Bing · 1 citation
#Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.0909.2391

Abstract

We study the evolution of anticanonical line bundles along the Kähler Ricci flow. We show that under some conditions, the convergence of Kähler Ricci flow is determined by the properties of the anticanonical divisors of M. As examples, the Kähler Ricci flow on M converges when M is a Fano surface and c₁²(M)=1 or c₁²(M)=3. Combined with the work in \citeCW1 and \citeCW2, this gives a Ricci flow proof of the Calabi conjecture on Fano surfaces with reductive automorphism groups. The original proof of this conjecture is due to Gang Tian.

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