Convergence of general inverse ${\sigma }_k$-flow on K\"{a}hler manifolds with Calabi Ansatz

We study the convergence behavior of the general inverse ${\sigma }_k$-flow on K"{a}hler manifolds with initial metrics satisfying the Calabi Ansatz. The limiting metrics can be either smooth or singular. In the latter case, interesting conic singularities along negatively self-intersected sub-varieties are formed as a result of partial blow-up.