On fundamental groups of algebraic varieties and value distribution theory
Annales de l'Institut Fourier, Volume 60 (2010) no. 2, pp. 551-563.

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

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

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
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, Volume 60 (2010) no. 2, pp. 551-563. doi : 10.5802/aif.2532. http://www.numdam.org/articles/10.5802/aif.2532/

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