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Donu Arapura
Toward the structure of fibered fundamental groups of projective varieties
(Vers la structure des groupes fondamentaux fibrés des variétés projectives)
Journal de l'École polytechnique — Mathématiques, 4 (2017), p. 595-611, doi: 10.5802/jep.52
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Class. Math.: 14H30
Mots clés: Groupe de Kähler, groupe de Mumford-Tate

Résumé - Abstract

Le groupe fondamental d’une variété projective lisse est dit fibré s’il s’envoie surjectivement sur celui d’une courbe de genre $2$ ou plus. Le but de cet article est d’établir des restrictions fortes sur ces groupes, et en particulier sur ceux des surfaces de Kodaira. Dans le cas spécifique d’une surface de Kodaira, ces résultats se présentent sous la forme de restrictions sur la représentation de monodromie dans le ‘mapping class group’. Lorsque la représentation de monodromie se compose de certaines représentations standard, les images sont Zariski denses dans un groupe semi-simple de type hermitien.

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