Explicit Kodaira-Spencer maps over PEL Shimura varieties

TL;DR

This paper constructs explicit morphisms between canonical line bundles on PEL Shimura varieties using Kodaira--Spencer maps, enabling comparison of line bundles and height functions.

Contribution

It provides a concrete method to explicitly compute morphisms between line bundles on integral models of PEL Shimura varieties.

Findings

Constructed explicit morphisms between line bundles using Kodaira--Spencer maps

Computed effects on canonical metrics of line bundles

Established a relationship between height functions from these line bundles

Abstract

The goal of our work is to construct a class of morphisms between two canonical line bundles on integral models of PEL Shimura varieties via Kodaira--Spencer maps, and explicitly compute such morphisms and their effects on the canonical metrics of line bundles. This result provides a concrete method for comparing two canonical line bundles and the corresponding arithmetic intersection numbers. In particular, it allows us to give an explicit relationship between the height functions defined by these two line bundles.