We determine which algebraic surface of logarithmic irregularity admit an algebraically non-degenerate entire curve.
Nous déterminons les surfaces algébriques d’irregularité logarithmique qui admettent des courbes entières non-dégénérées.
Keywords: Entire curve, holomorphic map, logarithmic irregularity, complex surface
Mot clés : courbe entière, irrégularité logarithmique, surface complexe
@article{AIF_2011__61_4_1517_0, author = {Winkelmann, J\"org}, title = {Degeneracy of entire curves in log surfaces with $\bar{q}=2$}, journal = {Annales de l'Institut Fourier}, pages = {1517--1537}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {61}, number = {4}, year = {2011}, doi = {10.5802/aif.2649}, zbl = {1250.32016}, mrnumber = {2951502}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.2649/} }
TY - JOUR AU - Winkelmann, Jörg TI - Degeneracy of entire curves in log surfaces with $\bar{q}=2$ JO - Annales de l'Institut Fourier PY - 2011 SP - 1517 EP - 1537 VL - 61 IS - 4 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.2649/ DO - 10.5802/aif.2649 LA - en ID - AIF_2011__61_4_1517_0 ER -
%0 Journal Article %A Winkelmann, Jörg %T Degeneracy of entire curves in log surfaces with $\bar{q}=2$ %J Annales de l'Institut Fourier %D 2011 %P 1517-1537 %V 61 %N 4 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.2649/ %R 10.5802/aif.2649 %G en %F AIF_2011__61_4_1517_0
Winkelmann, Jörg. Degeneracy of entire curves in log surfaces with $\bar{q}=2$. Annales de l'Institut Fourier, Volume 61 (2011) no. 4, pp. 1517-1537. doi : 10.5802/aif.2649. http://www.numdam.org/articles/10.5802/aif.2649/
[1] Compact manifolds in hyperbolicity, Trans. Amer. Math. Soc., Volume 235 (1978), pp. 213-219 | MR | Zbl
[2] Double sections, dominating maps, and the Jacobian fibration, Amer. J. Math., Volume 122 (2000) no. 5, pp. 1061-1084 | DOI | MR | Zbl
[3] Orbifoldes géométriques spéciales et classification biméromorphe des variétés kählériennes compactes (2008) (arxiv:0705.0737) | MR
[4] Logarithmic surfaces and hyperbolicity, Ann. Inst. Fourier (Grenoble), Volume 57 (2007) no. 5, pp. 1575-1610 | DOI | Numdam | MR | Zbl
[5] Endlichkeitssätze für abelsche Varietäten über Zahlkörpern, Invent. Math., Volume 73 (1983) no. 3, pp. 349-366 | DOI | MR | Zbl
[6] Density of integral points on algebraic varieties, Rational points on algebraic varieties (Progr. Math.), Volume 199, Birkhäuser, Basel, 2001, pp. 169-197 | MR | Zbl
[7] Characterization of abelian varieties, Compositio Math., Volume 43 (1981) no. 2, pp. 253-276 | Numdam | MR | Zbl
[8] Hyperbolic complex spaces, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 318, Springer-Verlag, Berlin, 1998 | MR | Zbl
[9] Lemma on logarithmic derivatives and holomorphic curves in algebraic varieties, Nagoya Math. J., Volume 83 (1981), pp. 213-233 | MR | Zbl
[10] Degeneracy of holomorphic curves into algebraic varieties, J. Math. Pures Appl. (9), Volume 88 (2007) no. 3, pp. 293-306 | MR | Zbl
[11] The second main theorem for holomorphic curves into semi-abelian varieties. II, Forum Math., Volume 20 (2008) no. 3, pp. 469-503 | DOI | MR | Zbl
[12] Diophantine approximations and value distribution theory, Lecture Notes in Mathematics, 1239, Springer-Verlag, Berlin, 1987 | MR | Zbl
[13] Integral points on subvarieties of semiabelian varieties. I, Invent. Math., Volume 126 (1996) no. 1, pp. 133-181 | DOI | MR | Zbl
[14] Integral points on subvarieties of semiabelian varieties. II, Amer. J. Math., Volume 121 (1999) no. 2, pp. 283-313 | DOI | MR | Zbl
[15] On a special class of complex tori, J. Lie Theory, Volume 16 (2006) no. 1, pp. 93-95 | MR | Zbl
[16] On Brody and entire curves, Bull. Soc. Math. France, Volume 135 (2007) no. 1, pp. 25-46 | Numdam | MR | Zbl
Cited by Sources: