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Nous développons une version de la théorie d’indice d’Atiyah pour les faisceaux cohérents sur les variétés algébriques lisses et l’utilisons pour attaquer certaines questions de J. Kollár.
Soit une variété complexe compacte projective algébrique lisse et connexe. Nous prouvons que si est un diviseur nef et gros, tel que la restriction de à la fibre générale d’une application de Shafarevich est effective, est effectif.
Soit une variété kählérienne compacte telle...
Let be a compact Kähler manifold, be a base point and be the monodromy representation of a -VHS. Building on Goldman–Millson’s classical
work, we construct a mixed Hodge structure on the complete local ring of the representation variety at and a variation of mixed Hodge structures whose monodromy is the universal deformation of .
Dans cette note nous établissons le résultat suivant, annoncé dans [CCE13] : si est l’image d’une représentation linéaire d’un groupe kählérien , il admet un sous-groupe d’indice fini qui est l’image d’une représentation linéaire du groupe fondamental d’une variété projective complexe lisse .
Il s’agit donc de la solution (à indice fini près) pour les représentations linéaires d’une question usuelle demandant si le groupe fondamental...
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