Modulus of a rational map into a commutative algebraic group

TL;DR

This paper introduces a notion of modulus for rational maps from higher-dimensional varieties to commutative algebraic groups, extending existing theories from curves to more complex varieties.

Contribution

It generalizes the concept of modulus for rational maps from curves to higher-dimensional algebraic varieties, providing new theoretical foundations.

Findings

Defined the modulus as an effective divisor on the variety

Established properties of the modulus in higher dimensions

Extended classical theories from curves to higher-dimensional cases

Abstract

For a rational map $\phi: X \to G$ from a normal algebraic variety $X$ to a commutative algebraic group $G$, we define the modulus of $\phi$ as an effective divisor on $X$. We study the properties of the modulus. This work generalizes the known theories for curves to higher dimensional varieties.