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

Nikita Klemyatin

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arXiv · 2411.17978

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

Nikita Klemyatin

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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.

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Nikita Klemyatin. 2024-11-27. Convergence of the inverse Monge-Ampere flow and Nadel multiplier ideal sheaves. https://arxiv.org/abs/2411.17978

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