# The Kähler Ricci flow on Fano manifolds (I)

Journal of the European Mathematical Society (2012)

- Volume: 014, Issue: 6, page 2001-2038
- ISSN: 1435-9855

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topChen, Xiuxiong, and Wang, Bing. "The Kähler Ricci flow on Fano manifolds (I)." Journal of the European Mathematical Society 014.6 (2012): 2001-2038. <http://eudml.org/doc/277303>.

@article{Chen2012,

abstract = {We study the evolution of pluri-anticanonical line bundles $K^\{-\nu \}_M$ 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 $c^2_1(M)=1$ or $c^2_1(M)=3$. 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].},

author = {Chen, Xiuxiong, Wang, Bing},

journal = {Journal of the European Mathematical Society},

language = {eng},

number = {6},

pages = {2001-2038},

publisher = {European Mathematical Society Publishing House},

title = {The Kähler Ricci flow on Fano manifolds (I)},

url = {http://eudml.org/doc/277303},

volume = {014},

year = {2012},

}

TY - JOUR

AU - Chen, Xiuxiong

AU - Wang, Bing

TI - The Kähler Ricci flow on Fano manifolds (I)

JO - Journal of the European Mathematical Society

PY - 2012

PB - European Mathematical Society Publishing House

VL - 014

IS - 6

SP - 2001

EP - 2038

AB - We study the evolution of pluri-anticanonical line bundles $K^{-\nu }_M$ 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 $c^2_1(M)=1$ or $c^2_1(M)=3$. 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].

LA - eng

UR - http://eudml.org/doc/277303

ER -

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