Geodesic
The Kähler Ricci flow on Fano manifolds (I)
Journal of the European Mathematical Society, Tome 14 (2012) no. 6, pp. 2001-2038

Voir la notice de l'article provenant de la source EMS Press

We study the evolution of pluri-anticanonical line bundles KM−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 c12​(M)=1 or c12​(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. The original proof of this conjecture is due to Gang Tian in [Tian90].
DOI : 10.4171/jems/353
Classification : 57-XX, 00-XX
Keywords: 
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     author = {Xiuxiong Chen and Bing Wang},
     title = {The {K\"ahler} {Ricci} flow on {Fano} manifolds {(I)}},
     journal = {Journal of the European Mathematical Society},
     pages = {2001--2038},
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     volume = {14},
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     year = {2012},
     doi = {10.4171/jems/353},
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}
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Xiuxiong Chen; Bing Wang. The Kähler Ricci flow on Fano manifolds (I). Journal of the European Mathematical Society, Tome 14 (2012) no. 6, pp. 2001-2038. doi: 10.4171/jems/353

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