Special holomorphic tensors on orthogonal modular varieties and applications to the Lang conjecture

TL;DR

This paper develops a method to construct special holomorphic tensors on orthogonal modular varieties using scalar-valued modular forms and applies this to address the Lang conjecture concerning the birational properties of subvarieties.

Contribution

It introduces a novel construction technique for holomorphic tensors on orthogonal modular varieties and applies it to problems related to the Lang conjecture.

Findings

Construction of special holomorphic tensors from scalar-valued modular forms

Applications to the Lang conjecture on subvarieties

Insights into the birational type of orthogonal modular varieties

Abstract

We introduce a method to construct special holomorphic tensors on orthogonal modular varieties from scalar-valued modular forms, and give applications to the Lang conjecture on the birational type of subvarieties of orthogonal modular varieties.