Modulus of a rational map into a commutative algebraic group

Abstract

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