Finite time singularities of the Ricci flow on compact Kähler surfaces are of Type I

Abstract

For any volume-collapsing finite-time singularity of a Kähler-Ricci flow on a compact Kähler surface, we show the flow satisfies a Type I curvature bound and classify the corresponding tangent flows. Combined with previous results, this shows that any finite-time singularity of a Kähler-Ricci flow on a compact Kähler surface is of Type I.

19 pages. Comments are welcome!