Blow-up rate of the scalar curvature along the conical K\"ahler-Ricci flow with finite time singularities

We investigate the scalar curvature behavior along the normalized conical K"ahler-Ricci flow ${\omega }_t$, which is the conic version of the normalized K"ahler-Ricci flow, with finite maximal existence time $T<\mathrm{\infty }$. We prove that the scalar curvature of ${\omega }_t$ is bounded from above by $C\mathrm{/}(T-t{)}^2$ under the existence of a contraction associated to the limiting cohomology class $[{\omega }_T]$. This generalizes Z. Zhang’s work to the conic case.