Modulus of a rational map into a commutative algebraic group

For a rational map $ϕ: X \to G$ from a normal algebraic variety $X$ to a commutative algebraic group $G$, we define the modulus of $ϕ$ 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.

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