Metric contraction of the cone divisor by the conical Kähler-Ricci flow

2017/04/02 by Edwards, Gregory · 1 citation
#35K55 (secondary) #53C44 (primary) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1704.00360

Abstract

We use the momentum construction of Calabi to study the conical Kähler-Ricci flow on Hirzebruch surfaces with cone angle along the exceptional curve, and show that either the flow Gromov-Hausdorff converges to the Riemann sphere or a single point in finite time, or the flow contracts the cone divisor to a single point and Gromov-Hausdorff converges to a two dimensional projective orbifold. This gives the first example of the conical Kähler-Ricci flow contracting the cone divisor to a single point. At the end, we introduce a conjectural picture of the geometry of finite time non-collapsing singularities of the flow on Kähler surfaces in general.

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