On the tangent flow to the collapsing Kähler-Ricci flow on Hirzebruch surfaces

2025/04/08 by Jiangtao Li, Li, Jiangtao
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2504.06471

openalex publication_date 2025/04/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

In this paper, we study the collpasing Kähler-Ricci flow on Hirzebruch surfaces, which develops finite time singularities. We show that any tangent flow based at a point in the singular time slice is the Kähler-Ricci flow associated with a nonflat gradient Kähler-Ricci shrinker with finitely many orbifold singularities .

Related

• Non-collapsed finite time singularities of the Ricci flow on compact Kähler surfaces are of Type I
• Metric contraction of the cone divisor by the conical Kähler-Ricci flow
• Scalar Curvature Behavior for Finite Time Singularity of Kähler-Ricci Flow
• Finite time singularities of the Kähler-Ricci flow
• The modified Kähler-Ricci flow, II