Convergence of the inverse Monge-Ampere flow and Nadel multiplier ideal sheaves

Abstract

We generalize the inverse Monge-Ampere flow, which was introduced in \cite{CHT17}, and provide conditions that guarantee the convergence of the flow without a priori assumption that $X$ has a Kähler-Einstein metric. We also show that if the underlying manifold does not admit Kähler-Einstein metric, then the flow develops Nadel multiplier ideal sheaves. In addition, we establish the linear lower bound for ${\inf }_X\phi$, and the theorem of Darvas and He for the inverse Monge-Ampere flow.

30 pages; v3: fixed some minor typos