Let X be a projective variety, possibly singular. A generalized Albanese variety of X was constructed by Esnault, Srinivas and Viehweg for algebraically closed base field as a universal regular quotient of a relative Chow group of 0-cycles of degree 0 modulo rational equivalence. In this paper, we obtain a functorial description of the Albanese of Esnault-Srinivas-Viehweg over a perfect base field, using duality theory of 1-motives with unipotent part.
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.Comment: 17 page
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