Degeneracy of entire curves in log surfaces with q ¯=2
[Dégénération des courbes entières dans les surfaces logarithmique avec q ¯=2]
Winkelmann, Jörg1
1 Rhur-Universität Bochum Mathematisches Institut Lehrstuhl Analysis II NA 4/73 44780 Bochum (Germany)
Annales de l'Institut Fourier, Tome 61 (2011) no. 4, pp. 1517-1537.

Nous déterminons les surfaces algébriques d’irregularité logarithmique 2 qui admettent des courbes entières non-dégénérées.

We determine which algebraic surface of logarithmic irregularity 2 admit an algebraically non-degenerate entire curve.

DOI : 10.5802/aif.2649
Classification : 32H25, 32H30
Keywords: Entire curve, holomorphic map, logarithmic irregularity, complex surface
Mot clés : courbe entière, irrégularité logarithmique, surface complexe
Winkelmann, Jörg 1

1 Rhur-Universität Bochum Mathematisches Institut Lehrstuhl Analysis II NA 4/73 44780 Bochum (Germany) 
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Winkelmann, Jörg. Degeneracy of entire curves in log surfaces with $\bar{q}=2$. Annales de l'Institut Fourier, Tome 61 (2011) no. 4, pp. 1517-1537. doi : 10.5802/aif.2649. http://www.numdam.org/articles/10.5802/aif.2649/

[1] Brody, Robert Compact manifolds in hyperbolicity, Trans. Amer. Math. Soc., Volume 235 (1978), pp. 213-219 | MR | Zbl

[2] Buzzard, Gregery T.; Lu, Steven S.-Y. Double sections, dominating maps, and the Jacobian fibration, Amer. J. Math., Volume 122 (2000) no. 5, pp. 1061-1084 | DOI | MR | Zbl

[3] Campana, F Orbifoldes géométriques spéciales et classification biméromorphe des variétés kählériennes compactes (2008) (arxiv:0705.0737) | MR

[4] Dethloff, Gerd; Lu, Steven S.-Y. Logarithmic surfaces and hyperbolicity, Ann. Inst. Fourier (Grenoble), Volume 57 (2007) no. 5, pp. 1575-1610 | DOI | Numdam | MR | Zbl

[5] Faltings, G. Endlichkeitssätze für abelsche Varietäten über Zahlkörpern, Invent. Math., Volume 73 (1983) no. 3, pp. 349-366 | DOI | MR | Zbl

[6] Hassett, Brendan; Tschinkel, Yuri 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] Kawamata, Yujiro Characterization of abelian varieties, Compositio Math., Volume 43 (1981) no. 2, pp. 253-276 | Numdam | MR | Zbl

[8] Kobayashi, Shoshichi Hyperbolic complex spaces, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 318, Springer-Verlag, Berlin, 1998 | MR | Zbl

[9] Noguchi, Junjiro Lemma on logarithmic derivatives and holomorphic curves in algebraic varieties, Nagoya Math. J., Volume 83 (1981), pp. 213-233 | MR | Zbl

[10] Noguchi, Junjiro; Winkelmann, Jörg; Yamanoi, Katsutoshi Degeneracy of holomorphic curves into algebraic varieties, J. Math. Pures Appl. (9), Volume 88 (2007) no. 3, pp. 293-306 | MR | Zbl

[11] Noguchi, Junjiro; Winkelmann, Jörg; Yamanoi, Katsutoshi 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] Vojta, Paul Diophantine approximations and value distribution theory, Lecture Notes in Mathematics, 1239, Springer-Verlag, Berlin, 1987 | MR | Zbl

[13] Vojta, Paul Integral points on subvarieties of semiabelian varieties. I, Invent. Math., Volume 126 (1996) no. 1, pp. 133-181 | DOI | MR | Zbl

[14] Vojta, Paul Integral points on subvarieties of semiabelian varieties. II, Amer. J. Math., Volume 121 (1999) no. 2, pp. 283-313 | DOI | MR | Zbl

[15] Winkelmann, Jörg On a special class of complex tori, J. Lie Theory, Volume 16 (2006) no. 1, pp. 93-95 | MR | Zbl

[16] Winkelmann, Jörg On Brody and entire curves, Bull. Soc. Math. France, Volume 135 (2007) no. 1, pp. 25-46 | Numdam | MR | Zbl

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