Explicit Kodaira-Spencer map over Hilbert modular varieties

TL;DR

This paper explicitly computes the Kodaira-Spencer maps on Hilbert-Siegel and twisted Hilbert modular varieties, analyzing their impact on Hodge bundle metrics, generalizing previous results in the field.

Contribution

It provides a detailed explicit computation of the Kodaira-Spencer maps for these modular varieties, extending prior work to more general settings.

Findings

Explicit formulas for Kodaira-Spencer maps on Hilbert-Siegel varieties

Analysis of the impact on Hodge bundle metrics

Generalization of previous results to twisted varieties

Abstract

The goal of this paper is to explicitly compute the Kodaira-Spencer maps over Hilbert-Siegel modular varieties and twisted Hilbert modular varieties and their effects on the metrics of the Hodge bundle. Our result is a generalization of the result in \cite{arXiv:2205.11334}.