Collapsing of the line bundle mean curvature flow on Kähler surfaces

Ryosuke Takahashi

Published 2019-12-31Version 1

We study the line bundle mean curvature flow on K\"ahler surfaces under the hypercritical phase and a certain semipositivity condition. We naturally encounter such a condition when considering the blowup of K\"ahler surfaces. We show that the flow converges smoothly to a singular solution to the deformed Hermitian Yang-Mills equation away from a finite number of holomorphic curves of negative self-intersection on the surface.