Global higher order estimates for collapsing Calabi-Yau metrics on elliptic K3 surfaces
Wangjian Jian, Yalong Shi
TL;DR
This paper extends local estimates to global ones for collapsing Calabi-Yau metrics on elliptic K3 surfaces, and analyzes the blow-up limits of these metrics on singular fibers.
Contribution
It provides the first global higher order estimates for collapsing Calabi-Yau metrics on elliptic K3 surfaces and investigates their blow-up limits on singular fibers.
Findings
Established global higher order estimates for Calabi-Yau metrics.
Analyzed blow-up limits on singular fibers.
Enhanced understanding of metric degeneration on elliptic K3 surfaces.
Abstract
We improve Gross-Wilson's local estimates to global ones. As an application, we study the blow-up limits of the degenerating Calabi-Yau metrics on singular fibers.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Algebraic Geometry and Number Theory