Infinite time singularities of the Kähler-Ricci flow
By Valentino Tosatti, Yuguang Zhang. 2014
63 citations recorded by the source corpus.
We study the long-time behavior of the Kahler-Ricci flow on compact Kahler manifolds. We give an almost complete classification of the singularity type of the flow at infinity, depending only on the underlying complex structure. If the manifold is of intermediate Kodaira dimension and has semiample canonical bundle, so that it is fibered by Calabi-Yau varieties, we show that parabolic rescalings around any point on a smooth fiber converge smoothly to a unique limit, which is the product of a Ricci-flat metric on the fiber and of a flat metric on Euclidean space. An analogous result holds for collapsing limits of Ricci-flat Kahler metrics.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/e2acaad67376bd0ed40d22ecdf2d5049225550b6
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
- Xiaokui Yang
- Valentino Tosatti
- B. Weinkove
- G'abor Sz'ekelyhidi
- Duong H. Phong
- Fang Zheng
- Dat T. To
- M. Gill
In Geometry and Topology
- Xiaokui Yang
- Valentino Tosatti
- B. Weinkove
- G'abor Sz'ekelyhidi
- Duong H. Phong
- Fang Zheng
- Dat T. To
- M. Gill
Citations in the corpus
- The Kähler-Ricci flow, Ricci-flat metrics and collapsing limits (2014, background): “The statement that eω|Xy → ωSRF,y (which can be improved to the smooth topology [60]) solves [55, Question 4.”