Finite-Time Singularities of the Kähler--Ricci Flow on Fano Bundles II
Wangjian Jian, Jian Song
Abstract
The analytic minimal model program proposed in SongTianSingularities, JST seeks to describe the birational transitions and fibre collapsing of the Kähler--Ricci flow through the geometry of its singularities. A fundamental conjecture of JST predicts Type I bounds for the scalar curvature and diameter of every fibre contratced by the limiting cohomological class at the finite singular time. This paper is a continuation of Splitting that establishes the Type I conjecture for collapsing solutions on Fano bundles with arbitrary smooth Fano fibres. If the fibre admits a smooth Kähler-Einstein metric, the Type I bound holds for the full curvature tensor.
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