Some models for bubbling of (log) K\"ahler-Einstein metrics
Martin de Borbon, Cristiano Spotti
TL;DR
This paper explores the behavior of (log) K"ahler-Einstein metrics during degenerations, focusing on metric bubble trees in low dimensions and proposing a conjectural framework for higher dimensions.
Contribution
It provides a detailed analysis of metric bubble trees in complex dimensions one and two and introduces a conjectural model for higher-dimensional cases.
Findings
Characterization of bubble trees in low dimensions
Description of degeneration patterns of (log) K"ahler-Einstein metrics
Proposal of a higher-dimensional conjectural framework
Abstract
We investigate aspects of the metric bubble tree for non-collapsing degenerations of (log) K\"ahler-Einstein metrics in complex dimensions one and two, and further describe a conjectural higher dimensional picture.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Algebraic Geometry and Number Theory