On fundamental groups of algebraic varieties and value distribution theory

[Groupes fondamentaux des variétés algébriques et théorie de distributions des valeurs]

Yamanoi, Katsutoshi

Annales de l'Institut Fourier, Tome 60 (2010), p. 551-563 / Harvested from Numdam

Résumé

Si une variété $X$ projective lisse admet une application holomorphe non-dégénérée $\mathbb{C}\rightarrow X$ du plan complexe $\mathbb{C}$, alors pour chaque représentation linéaire de dimension finie du groupe fondamental de $X$ l’image de cette représentation est presque abélienne. Cela soutient une conjecture proposée par F. Campana, parue dans ce même journal en 2004.

Abstract

If a smooth projective variety $X$ admits a non-degenerate holomorphic map $\mathbb{C}\rightarrow X$ from the complex plane $\mathbb{C}$, then for any finite dimensional linear representation of the fundamental group of $X$ the image of this representation is almost abelian. This supports a conjecture proposed by F. Campana, published in this journal in 2004.

Détail

Publié le : 2010-01-01

MR 2667786 | Zbl 1193.32010

DOI : https://doi.org/10.5802/aif.2532
Classification:  32H30,  14F35
Mots clés: théorie de distributions des valeurs, application holomorphe, groupe fondamental, variété algébrique

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