Albanese varieties with modulus and Hodge theory
[Variété d’Albanese avec module et théorie de Hodge]
Kato, Kazuya ; Russell, Henrik
Annales de l'Institut Fourier, Tome 62 (2012), p. 783-806 / Harvested from Numdam
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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.

Publié le : 2012-01-01
DOI : https://doi.org/10.5802/aif.2694
Classification:  14L10,  14C30,  14F42
Mots clés: variété d’Albanese généralisée, module d’une fonction, structure de Hodge mixte généralisée 
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     author = {Kato, Kazuya and Russell, Henrik},
     title = {Albanese varieties with modulus and Hodge theory},
     journal = {Annales de l'Institut Fourier},
     volume = {62},
     year = {2012},
     pages = {783-806},
     doi = {10.5802/aif.2694},
     zbl = {1261.14023},
     mrnumber = {2985516},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_2012__62_2_783_0}
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Kato, Kazuya; Russell, Henrik. Albanese varieties with modulus and Hodge theory. Annales de l'Institut Fourier, Tome 62 (2012) pp. 783-806. doi : 10.5802/aif.2694. http://gdmltest.u-ga.fr/item/AIF_2012__62_2_783_0/

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