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

2024/11/27 by Nikita Klemyatin, Klemyatin, Nikita · 1 citation
Mathematics · #Geometry and complex manifolds #Algebraic Geometry and Number Theory #Advanced Topics in Algebra

paper · pdf · doi:10.48550/arxiv.2411.17978

Abstract

We generalize the inverse Monge-Ampere flow, which was introduced in \citeCHT17, 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_Xφ, and the theorem of Darvas and He for the inverse Monge-Ampere flow.

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