The Kähler Ricci flow on Fano manifolds (I)

Chen, 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 -