Convergence of Calabi-Yau manifolds
Wei-Dong Ruan, Yuguang Zhang
TL;DR
This paper investigates how Calabi-Yau manifolds converge under various degenerations, including orbifold and canonical singularities, and examines their collapsing behavior.
Contribution
It provides new insights into the convergence and collapsing phenomena of Calabi-Yau manifolds during degenerations.
Findings
Calabi-Yau manifolds can degenerate to orbifold and canonical singularities.
The paper characterizes the collapsing behavior of Calabi-Yau families.
Results contribute to understanding geometric limits of Calabi-Yau spaces.
Abstract
In this paper, we study the convergence of Calabi-Yau manifolds under K\"{a}hler degeneration to orbifold singularities and complex degeneration to canonical singularities (including the conifold singularities), and the collapsing of a family of Calabi-Yau manifolds.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Algebraic Geometry and Number Theory