A finite-time singularity of Calabi flow

Disproves Chen's smooth long-time existence conjecture for Calabi flow by constructing a smooth $U(10)$-invariant Kähler metric on $\mathbb{CP}^{10}$ whose flow develops a finite-time singularity. The metric lies in the Fubini–Study class, so the failure occurs even in a class containing a constant-scalar-curvature metric.