Extremal cases for the log canonical threshold
Alexander Rashkovskii
TL;DR
This paper explores extremal cases for the log canonical threshold, linking recent results to the characterization of plurisubharmonic functions with specific Monge-Ampère mass and minimal thresholds.
Contribution
It provides a new description of plurisubharmonic functions with given Monge-Ampère mass and minimal log canonical threshold based on recent theoretical results.
Findings
Characterization of plurisubharmonic functions with minimal log canonical threshold
Analysis of equality cases in related inequalities
Extension of recent theoretical results to extremal cases
Abstract
We show that a recent result of Demailly and Pham Hoang Hiep \cite{DH} implies a description of plurisubharmonic functions with given Monge-Amp\`ere mass and smallest possible log canonical threshold. We also study an equality case for the inequality from \cite{DH}.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Algebraic Geometry and Number Theory