On Brody and entire curves

Jörg Winkelmann

Bulletin de la Société Mathématique de France (2007)

  • Volume: 135, Issue: 1, page 25-46
  • ISSN: 0037-9484

Abstract

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We discuss an example of an open subset of a torus which admits a dense entire curve, but no dense Brody curve.

How to cite

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Winkelmann, Jörg. "On Brody and entire curves." Bulletin de la Société Mathématique de France 135.1 (2007): 25-46. <http://eudml.org/doc/272472>.

@article{Winkelmann2007,
abstract = {We discuss an example of an open subset of a torus which admits a dense entire curve, but no dense Brody curve.},
author = {Winkelmann, Jörg},
journal = {Bulletin de la Société Mathématique de France},
keywords = {Brody lemma; entire curve; hyperbolicity; abelian variety},
language = {eng},
number = {1},
pages = {25-46},
publisher = {Société mathématique de France},
title = {On Brody and entire curves},
url = {http://eudml.org/doc/272472},
volume = {135},
year = {2007},
}

TY - JOUR
AU - Winkelmann, Jörg
TI - On Brody and entire curves
JO - Bulletin de la Société Mathématique de France
PY - 2007
PB - Société mathématique de France
VL - 135
IS - 1
SP - 25
EP - 46
AB - We discuss an example of an open subset of a torus which admits a dense entire curve, but no dense Brody curve.
LA - eng
KW - Brody lemma; entire curve; hyperbolicity; abelian variety
UR - http://eudml.org/doc/272472
ER -

References

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  1. [1] N. U. Arakeljan – « Approximation complexe et propriétés des fonctions analytiques », in Actes du Congrès International des Mathématiciens (Nice, 1970), Tome 2, vol. 2, Gauthier-Villars, 1971, p. 595–600. Zbl0234.30029MR422623
  2. [2] A. Bloch – « Sur les systèmes de fonctions uniformes satisfaisant à l’equation d’une variété algébrique dont l’irrégularité dépasse la dimension », J. Math. Pures Appl.5 (1926), p. 19–66. Zbl52.0373.04JFM52.0373.04
  3. [3] R. Brody – « Compact manifolds in hyperbolicity », Trans. Amer. Math. Soc.235 (1978), p. 213–219. Zbl0416.32013MR470252
  4. [4] F. Campana – « Orbifolds, special varieties and classification theory », Ann. Inst. Fourier (Grenoble) 54 (2004), p. 499–630. Zbl1062.14014MR2097416
  5. [5] G. Faltings – « Endlichkeitssätze für abelsche Varietäten über Zahlkörpern », Invent. Math.73 (1983), p. 349–366. Zbl0588.14026MR718935
  6. [6] Y. Kawamata – « On Bloch’s conjecture », Invent. Math.57 (1980), p. 97–100. Zbl0569.32012MR564186
  7. [7] S. Kobayashi – Hyperbolic complex spaces, Grundlehren der Mathematischen Wissenschaften, vol. 318, Springer, 1998. Zbl0917.32019MR1635983
  8. [8] S. Lang – Introduction to complex hyperbolic spaces, Springer, 1987. Zbl0628.32001MR886677
  9. [9] —, Number theory. III, Encyclopaedia of Mathematical Sciences, vol. 60, Springer, 1991, Diophantine geometry. Zbl0744.14012MR1112552
  10. [10] H. L. Royden – « Remarks on the Kobayashi metric », in Several complex variables, II (Proc. Internat. Conf., Univ. Maryland, College Park, Md., 1970), Lecture Notes in Math., vol. 185, Springer, 1971, p. 125–137. Lecture Notes in Math., Vol. 185. Zbl0218.32012MR304694
  11. [11] P. Vojta – Diophantine approximations and value distribution theory, Lecture Notes in Mathematics, vol. 1239, Springer, 1987. Zbl0609.14011MR883451
  12. [12] L. Zalcman – « Normal families: new perspectives », Bull. Amer. Math. Soc. (N.S.) 35 (1998), p. 215–230. Zbl1037.30021MR1624862

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