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

TL;DR

This paper extends the inverse Monge-Ampere flow, providing convergence conditions and linking flow behavior to the existence of Kähler-Einstein metrics and Nadel multiplier ideal sheaves.

Contribution

It generalizes the inverse Monge-Ampere flow and establishes new convergence criteria without assuming the existence of Kähler-Einstein metrics.

Findings

Flow converges under new conditions

Flow develops Nadel multiplier ideal sheaves when no Kähler-Einstein metric exists

Established linear lower bound for the infimum of 

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 K\"ahler-Einstein metric. We also show that if the underlying manifold does not admit K\"ahler-Einstein metric, then the flow develops Nadel multiplier ideal sheaves. In addition, we establish the linear lower bound for $\inf_X\varphi$, and the theorem of Darvas and He for the inverse Monge-Ampere flow.