On fundamental groups of algebraic varieties and value distribution theory

Katsutoshi Yamanoi[1]

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

Annales de l’institut Fourier (2010)

  • Volume: 60, Issue: 2, page 551-563
  • ISSN: 0373-0956

Abstract

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If a smooth projective variety X admits a non-degenerate holomorphic map ℂ → 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.

How to cite

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Yamanoi, Katsutoshi. "On fundamental groups of algebraic varieties and value distribution theory." Annales de l’institut Fourier 60.2 (2010): 551-563. <http://eudml.org/doc/116281>.

@article{Yamanoi2010,
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.},
affiliation = {Kumamoto University Graduate School of Science and Technology Kurokami, Kumamoto 860-8555 (Japan)},
author = {Yamanoi, Katsutoshi},
journal = {Annales de l’institut Fourier},
keywords = {Value distribution theory; holomorphic map; fundamental group; algebraic variety; value distribution theory; entire curve},
language = {eng},
number = {2},
pages = {551-563},
publisher = {Association des Annales de l’institut Fourier},
title = {On fundamental groups of algebraic varieties and value distribution theory},
url = {http://eudml.org/doc/116281},
volume = {60},
year = {2010},
}

TY - JOUR
AU - Yamanoi, Katsutoshi
TI - On fundamental groups of algebraic varieties and value distribution theory
JO - Annales de l’institut Fourier
PY - 2010
PB - Association des Annales de l’institut Fourier
VL - 60
IS - 2
SP - 551
EP - 563
AB - 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.
LA - eng
KW - Value distribution theory; holomorphic map; fundamental group; algebraic variety; value distribution theory; entire curve
UR - http://eudml.org/doc/116281
ER -

References

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  17. Katsutoshi Yamanoi, Holomorphic curves in abelian varieties and intersections with higher codimensional subvarieties II Zbl1073.32007
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