Degeneration of Ricci-flat Calabi-Yau manifolds and its applications
Yuguang Zhang
TL;DR
This survey reviews recent advances in understanding how Ricci-flat Kähler-Einstein metrics behave during degenerations of Calabi-Yau manifolds, highlighting key developments and applications.
Contribution
It compiles and discusses recent progress in the study of metric degeneration of Ricci-flat Calabi-Yau manifolds, providing a comprehensive overview.
Findings
Descriptions of metric degeneration patterns
Connections to algebraic geometry and moduli spaces
Implications for string theory and mirror symmetry
Abstract
This is a survey article of the recent progresses on the metric behaviour of Ricci-flat K\"{a}hler-Einstein metrics along degenerations of Calabi-Yau manifolds.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Advanced Differential Geometry Research