## Journal of Mathematics of Kyoto University

### Generalized albanese and its dual

Henrik Russell

#### Abstract

Let $X$ be a projective variety over an algebraically closed field $k$ of characteristic 0.We consider categories of rational maps from $X$ to commutative algebraic groups, and ask for objects satisfying the universal mapping property.A necessary and sufficient condition for the existence of such universal objects is given, as well as their explicit construction, using duality theory of generalized 1-motives. An important application is the Albanese of a singular projective variety, which was constructed by Esnault, Srinivas and Viehweg as a universal regular quotient of a relative Chow group of 0-cycles of degree 0 modulo rational equivalence.We obtain functorial descriptions of the universal regular quotient and its dual 1-motive.

#### Article information

Source
J. Math. Kyoto Univ., Volume 48, Number 4 (2008), 907-949.

Dates
First available in Project Euclid: 14 August 2009

https://projecteuclid.org/euclid.kjm/1250271323

Digital Object Identifier
doi:10.1215/kjm/1250271323

Mathematical Reviews number (MathSciNet)
MR2513591

Zentralblatt MATH identifier
1170.14005

#### Citation

Russell, Henrik. Generalized albanese and its dual. J. Math. Kyoto Univ. 48 (2008), no. 4, 907--949. doi:10.1215/kjm/1250271323. https://projecteuclid.org/euclid.kjm/1250271323