scholarly journals Multiplier ideal sheaves and the Kähler–Ricci flow on toric Fano manifolds with large symmetry

2012 ◽  
Vol 20 (2) ◽  
pp. 341-368
Author(s):  
Yuji Sano
Keyword(s):  
Ricci Flow ◽  
Fano Manifolds ◽  
Ideal Sheaves ◽  
Multiplier Ideal

scholarly journals Multiplier ideal sheaves and integral invariants on toric Fano manifolds

2010 ◽  
Vol 350 (2) ◽  
pp. 245-267
Author(s):  
Akito Futaki ◽  
Yuji Sano
Keyword(s):  
Fano Manifolds ◽  
Integral Invariants ◽  
Ideal Sheaves ◽  
Multiplier Ideal

scholarly journals Multiplier ideal sheaves and the Kähler-Ricci flow

2007 ◽  
Vol 15 (3) ◽  
pp. 613-632 ◽  
Author(s):  
D.H. Phong ◽  
Natasa Sesum ◽  
Jacob Sturm
Keyword(s):  
Ricci Flow ◽  
Ideal Sheaves ◽  
Multiplier Ideal

scholarly journals Characterization of multiplier ideal sheaves with weights of Lelong number one

2015 ◽  
Vol 285 ◽  
pp. 1688-1705 ◽  
Author(s):  
Qi'an Guan ◽  
Xiangyu Zhou
Keyword(s):  
Lelong Number ◽  
Ideal Sheaves ◽  
Multiplier Ideal

scholarly journals Kähler–Einstein metrics and the Kähler–Ricci flow on log Fano varieties

2019 ◽  
Vol 2019 (751) ◽  
pp. 27-89 ◽  
Author(s):  
Robert J. Berman ◽  
Sebastien Boucksom ◽  
Philippe Eyssidieux ◽  
Vincent Guedj ◽  
Ahmed Zeriahi
Keyword(s):  
Ricci Flow ◽  
Existence And Uniqueness ◽  
Additional Condition ◽  
Einstein Metrics ◽  
Discrete Version ◽  
Fano Varieties ◽  
Fano Manifolds ◽  
Smooth Convergence ◽  
Kähler Einstein Metrics ◽  
Special Case

AbstractWe prove the existence and uniqueness of Kähler–Einstein metrics on {{\mathbb{Q}}}-Fano varieties with log terminal singularities (and more generally on log Fano pairs) whose Mabuchi functional is proper. We study analogues of the works of Perelman on the convergence of the normalized Kähler–Ricci flow, and of Keller, Rubinstein on its discrete version, Ricci iteration. In the special case of (non-singular) Fano manifolds, our results on Ricci iteration yield smooth convergence without any additional condition, improving on previous results. Our result for the Kähler–Ricci flow provides weak convergence independently of Perelman’s celebrated estimates.

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