Contracting exceptional divisors by the Kähler–Ricci flow II
By Jian Song, B. Weinkove. 2010
102 citations recorded by the source corpus.
We investigate the case of the Kähler–Ricci flow blowing down disjoint exceptional divisors with normal bundle 𝒪(−k) to orbifold points. We prove smooth convergence outside the exceptional divisors and global Gromov–Hausdorff convergence. Moreover, we prove a conjecture of the authors by establishing the result that the Gromov–Hausdorff limit coincides with the metric completion of the limiting metric under the flow. This improves and extends the previous work of the authors. We apply this to ℙ1‐bundles which are higher‐dimensional analogues of the Hirzebruch surfaces. We also consider the case of a minimal surface of general type with only distinct irreducible (−2)‐curves and show that solutions to the normalized Kähler–Ricci flow converge in the Gromov–Hausdorff sense to a Kähler–Einstein orbifold.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/6e0e3d0517c1421815a14fa5fbd2979a42132e8d
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
- Xiuxiong Chen
- Duong H. Phong
- Bing Wang
- Jian Song
In Geometry and Topology
- Xiaokui Yang
- B. Weinkove
- Valentino Tosatti
- G'abor Sz'ekelyhidi
- Duong H. Phong
- Xiuxiong Chen
- Bing Wang
- Jian Song
Citations in the corpus
- Space of Ricci Flows I (2009, background): “For other important progress in Kähler Ricci flow, we refer interested readers to the following papers(far away from being complete): [72], [110], [109], [101], [111], [79], [101], [78], [68], [104], [88], as well as references listed therein.”
- The Kähler-Ricci flow, Ricci-flat metrics and collapsing limits (2014, methodology): “According to the analytic minimal model program [39, 50, 40, 42] the Kähler-Ricci flow will perform a surgery at each finite time singularity, corresponding to a birational operation of the minimal model program from algebraic geometry, and arrive at the minimal model Xmin with nef canonical bundle ”
- Interior derivative estimates for the Kähler–Ricci flow (2011, unknown): “2 gives an alternative proof of the results in Section 4 of [Song and Weinkove 2011b].”