Explicit Kodaira-Spencer map over Shimura Curves
Xinyi Yuan
TL;DR
This paper explicitly computes the Kodaira-Spencer map for quaternionic Shimura curves over Q and analyzes its impact on the Hodge bundle metrics, providing detailed insights into their geometric structure.
Contribution
It offers an explicit calculation of the Kodaira-Spencer map for quaternionic Shimura curves, a result previously known only to experts.
Findings
Explicit formula for the Kodaira-Spencer map derived
Impact on Hodge bundle metrics clarified
Enhances understanding of Shimura curve geometry
Abstract
The goal of this paper is to explicitly compute the Kodaira-Spencer map for a quaternionic Shimura curve over Q and its effect on the metrics of the Hodge bundle. The results are known to experts.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Geometry and complex manifolds · Advanced Algebra and Geometry