Convergence of general inverse ${\sigma }_k$-flow on Kähler manifolds with Calabi Ansatz

Abstract

We study the convergence behavior of the general inverse ${\sigma }_k$-flow on Kähler 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.

References in corpus (3)

• The Kahler-Ricci flow through singularities
• On rotationally symmetric Kahler-Ricci solitons
• On the geometric flows solving Kählerian inverse ${\sigma }_k$ equations