Non-collapsed finite time singularities of the Ricci flow on compact Kähler surfaces are of Type I

Abstract

We show that any non-collapsed finite time singularity of the Ricci flow on a compact Kähler surface is of Type I. Combined with a previous result of the first author, Cifarelli, and Deruelle, it follows that any such singularity is modeled on the shrinking Ricci soliton of Feldman-Ilmanen-Knopf on the total space of the line bundle ${\mathcal{O}}_{{\mathbb{P}}^1}(-1)\to {\mathbb{P}}^1$.

46 pages; Theorem 4.4 added