Albanese varieties with modulus and Hodge theory
Annales de l'Institut Fourier, Volume 62 (2012) no. 2, pp. 783-806.

Let X be a proper smooth variety over a field k of characteristic 0 and Y an effective divisor on X with multiplicity. We introduce a generalized Albanese variety Alb(X,Y) of X of modulus Y, as higher dimensional analogue of the generalized Jacobian with modulus of Rosenlicht-Serre. Our construction is algebraic. For k= we give a Hodge theoretic description.

Soient X une variété propre et lisse sur un corps k de caractéristique 0 et Y un diviseur effectif avec multiplicité sur X. Nous introduisons une variété d’Albanese généralisée Alb(X,Y) de X, de module Y, comme analogue en dimension supérieure de la jacobienne généralisée avec module de Rosenlicht-Serre. Notre construction est algébrique. Si k=, nous donnons une description en termes de théorie de Hodge.

DOI: 10.5802/aif.2694
Classification: 14L10, 14C30, 14F42
Keywords: generalized Albanese variety, modulus of a rational map, generalized mixed Hodge structure
Mot clés : variété d’Albanese généralisée, module d’une fonction, structure de Hodge mixte généralisée
Kato, Kazuya 1; Russell, Henrik 2

1 University of Chicago Department of Mathematics Chicago, IL 60637 (USA)
2 Universität Duisburg-Essen FB6 Mathematik, Campus Essen 45117 Essen (Germany)
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Kato, Kazuya; Russell, Henrik. Albanese varieties with modulus and Hodge theory. Annales de l'Institut Fourier, Volume 62 (2012) no. 2, pp. 783-806. doi : 10.5802/aif.2694. http://www.numdam.org/articles/10.5802/aif.2694/

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