Class number relations arising from intersections of Shimura curves and Humbert surfaces

TL;DR

This paper derives new class number relations by studying intersections of Shimura curves and Humbert surfaces on Siegel modular threefolds, extending classical relations to higher dimensions.

Contribution

It introduces a higher-dimensional analogue of the Hurwitz-Kronecker class number relation through geometric intersection analysis.

Findings

New class number relations derived from geometric intersections

Extension of classical relations to higher-dimensional settings

Provides a framework for further exploration of modular varieties

Abstract

By considering the intersections of Shimura curves and Humbert surfaces on the Siegel modular threefold, we obtain new class number relations. The result is a higher-dimensional analogue of the classical Hurwitz-Kronecker class number relation.