On fundamental groups of algebraic varieties and value distribution theory

Yamanoi, Katsutoshi

doi:10.5802/aif.2532

On fundamental groups of algebraic varieties and value distribution theory
[Groupes fondamentaux des variétés algébriques et théorie de distributions des valeurs]

Yamanoi, Katsutoshi ¹

¹ Kumamoto University Graduate School of Science and Technology Kurokami, Kumamoto 860-8555 (Japan)

Annales de l'Institut Fourier, Tome 60 (2010) no. 2, pp. 551-563.

Résumé
Abstract

Si une variété $X$ projective lisse admet une application holomorphe non-dégénérée $ℂ \to X$ du plan complexe $ℂ$ , 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.

If a smooth projective variety $X$ admits a non-degenerate holomorphic map $ℂ \to X$ from the complex plane $ℂ$ , 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.

MR Zbl

DOI : 10.5802/aif.2532

Classification : 32H30, 14F35
Keywords: Value distribution theory, holomorphic map, fundamental group, algebraic variety
Mot clés : théorie de distributions des valeurs, application holomorphe, groupe fondamental, variété algébrique

Affiliations des auteurs :

Yamanoi, Katsutoshi ¹

¹ Kumamoto University Graduate School of Science and Technology Kurokami, Kumamoto 860-8555 (Japan)

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Yamanoi, Katsutoshi. On fundamental groups of algebraic varieties and value distribution theory. Annales de l'Institut Fourier, Tome 60 (2010) no. 2, pp. 551-563. doi : 10.5802/aif.2532. https://www.numdam.org/articles/10.5802/aif.2532/

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