The Kähler-Ricci flow on Fano bundles

2016/10/11 by Xin Fu, Fu, Xin, Shijin Zhang +1
Mathematics · #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1610.03366

openalex publication_date 2016/10/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the behavior of the Kähler-Ricci flow on some Fano bundle which is a trivial bundle on one Zariski open set. We show that if the fiber is ℙ^m blown up at one point or some weighted projective space blown up at the orbifold point and the initial metric is in a suitable kähler class, then the fibers collapse in finite time and the metrics converge sub-sequentially in Gromov-Hausdorff sense to a metric on the base.

Citations

• Finite extinction time for the solutions to the Ricci flow on certain three-manifolds

Related

• The Kähler-Ricci flow, holomorphic vector fields and Fano bundles
• On the Kahler-Ricci flow on Fano manifolds
• Kähler Ricci flow on Fano surfaces (I)
• Fano Fibrations and Twisted Kähler-Einstein Metrics II: The Kähler-Ricci Flow
• Finite time singularities of the Kähler-Ricci flow