Si une variété projective lisse admet une application holomorphe non-dégénérée du plan complexe , alors pour chaque représentation linéaire de dimension finie du groupe fondamental de 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 admits a non-degenerate holomorphic map from the complex plane , then for any finite dimensional linear representation of the fundamental group of the image of this representation is almost abelian. This supports a conjecture proposed by F. Campana, published in this journal in 2004.
Keywords: Value distribution theory, holomorphic map, fundamental group, algebraic variety
Mot clés : théorie de distributions des valeurs, application holomorphe, groupe fondamental, variété algébrique
@article{AIF_2010__60_2_551_0, author = {Yamanoi, Katsutoshi}, title = {On fundamental groups of algebraic varieties and value distribution theory}, journal = {Annales de l'Institut Fourier}, pages = {551--563}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {60}, number = {2}, year = {2010}, doi = {10.5802/aif.2532}, zbl = {1193.32010}, mrnumber = {2667786}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.2532/} }
TY - JOUR AU - Yamanoi, Katsutoshi TI - On fundamental groups of algebraic varieties and value distribution theory JO - Annales de l'Institut Fourier PY - 2010 SP - 551 EP - 563 VL - 60 IS - 2 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.2532/ DO - 10.5802/aif.2532 LA - en ID - AIF_2010__60_2_551_0 ER -
%0 Journal Article %A Yamanoi, Katsutoshi %T On fundamental groups of algebraic varieties and value distribution theory %J Annales de l'Institut Fourier %D 2010 %P 551-563 %V 60 %N 2 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.2532/ %R 10.5802/aif.2532 %G en %F AIF_2010__60_2_551_0
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. http://www.numdam.org/articles/10.5802/aif.2532/
[1] Réseaux arithmétiques et commensurateur d’après G. A. Margulis, Invent. Math., Volume 116 (1994) no. 1-3, pp. 1-25 | DOI | MR | Zbl
[2] Algebraic surfaces holomorphically dominable by , Invent. Math., Volume 139 (2000) no. 3, pp. 617-659 | DOI | MR | Zbl
[3] Ensembles de Green-Lazarsfeld et quotients résolubles des groupes de Kähler, J. Algebraic Geom., Volume 10 (2001) no. 4, pp. 599-622 | MR | Zbl
[4] Orbifolds, special varieties and classification theory, Ann. Inst. Fourier (Grenoble), Volume 54 (2004) no. 3, pp. 499-630 | DOI | Numdam | MR | Zbl
[5] Sur la convexité holomorphe des revêtements linéaires réductifs d’une variété projective algébrique complexe, Invent. Math., Volume 156 (2004) no. 3, pp. 503-564 | DOI | MR | Zbl
[6] Locally homogeneous complex manifolds, Acta Math., Volume 123 (1969), pp. 253-302 | DOI | MR | Zbl
[7] Recent developments in Hodge theory: a discussion of techniques and results, Discrete subgroups of Lie groups and applicatons to moduli (Internat. Colloq., Bombay, 1973), Oxford Univ. Press, Bombay, 1975, pp. 31-127 | MR | Zbl
[8] Harmonic maps into singular spaces and -adic superrigidity for lattices in groups of rank one, Inst. Hautes Études Sci. Publ. Math. (1992) no. 76, pp. 165-246 | DOI | Numdam | MR | Zbl
[9] Harmonic maps into Bruhat-Tits buildings and factorizations of -adically unbounded representations of of algebraic varieties. I, J. Algebraic Geom., Volume 9 (2000) no. 1, pp. 1-42 | MR | Zbl
[10] On the Shafarevich maps, Algebraic geometry—Santa Cruz 1995 (Proc. Sympos. Pure Math.), Volume 62, Amer. Math. Soc., Providence, RI, 1997, pp. 173-216 | MR | Zbl
[11] Shafarevich maps and plurigenera of algebraic varieties, Invent. Math., Volume 113 (1993) no. 1, pp. 177-215 | DOI | MR | Zbl
[12] Meromorphic mappings of a covering space over into a projective variety and defect relations, Hiroshima Math. J., Volume 6 (1976) no. 2, pp. 265-280 | MR | Zbl
[13] On the value distribution of meromorphic mappings of covering spaces over into algebraic varieties, J. Math. Soc. Japan, Volume 37 (1985) no. 2, pp. 295-313 | DOI | MR | Zbl
[14] Geometric function theory in several complex variables, Translations of Mathematical Monographs, 80, American Mathematical Society, Providence, RI, 1990 (Translated from the Japanese by Noguchi) | MR | Zbl
[15] Degeneracy of holomorphic curves into algebraic varieties, J. Math. Pures Appl. (9), Volume 88 (2007) no. 3, pp. 293-306 | MR | Zbl
[16] Higgs bundles and local systems, Inst. Hautes Études Sci. Publ. Math. (1992) no. 75, pp. 5-95 | DOI | Numdam | MR | Zbl
[17] Holomorphic curves in abelian varieties and intersections with higher codimensional subvarieties II (preprint)
[18] Holomorphic curves in abelian varieties and intersections with higher codimensional subvarieties, Forum Math., Volume 16 (2004) no. 5, pp. 749-788 | DOI | MR | Zbl
[19] Ergodic theory and semisimple groups, Monographs in Mathematics, 81, Birkhäuser Verlag, Basel, 1984 | MR | Zbl
[20] Kodaira dimension and Chern hyperbolicity of the Shafarevich maps for representations of of compact Kähler manifolds, J. Reine Angew. Math., Volume 472 (1996), pp. 139-156 | DOI | MR | Zbl
[21] Representations of fundamental groups of algebraic varieties, Lecture Notes in Mathematics, 1708, Springer-Verlag, Berlin, 1999 | MR | Zbl
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