Albanese varieties with modulus and Hodge theory

Kato, Kazuya; Russell, Henrik

doi:10.5802/aif.2694

Albanese varieties with modulus and Hodge theory
[Variété d’Albanese avec module et théorie de Hodge]

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)

Annales de l'Institut Fourier, Tome 62 (2012) no. 2, pp. 783-806.

Résumé
Abstract

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 $k = ℂ$ , nous donnons une description en termes de théorie de Hodge.

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 $k = ℂ$ we give a Hodge theoretic description.

MR Zbl

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

Affiliations des auteurs :

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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     title = {Albanese varieties with modulus and {Hodge} theory},
     journal = {Annales de l'Institut Fourier},
     pages = {783--806},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {62},
     number = {2},
     year = {2012},
     doi = {10.5802/aif.2694},
     zbl = {1261.14023},
     mrnumber = {2985516},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/aif.2694/}
}

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Kato, Kazuya; Russell, Henrik. Albanese varieties with modulus and Hodge theory. Annales de l'Institut Fourier, Tome 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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