Degeneracy of entire curves in log surfaces with $\bar{q}=2$

Winkelmann, Jörg

Degeneracy of entire curves in log surfaces with

\bar{q} = 2

Winkelmann, Jörg

Annales de l'Institut Fourier, Volume 61 (2011) no. 4, p. 1517-1537

Abstract
Résumé

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

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

MR 2951502 | Zbl 1250.32016

DOI : https://doi.org/10.5802/aif.2649
Classification: 32H25, 32H30
Keywords: Entire curve, holomorphic map, logarithmic irregularity, complex surface

@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},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {61},
     number = {4},
     year = {2011},
     pages = {1517-1537},
     doi = {10.5802/aif.2649},
     mrnumber = {2951502},
     zbl = {1250.32016},
     language = {en},
     url = {http://www.numdam.org/item/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/item/AIF_2011__61_4_1517_0/

References

[1] Brody, Robert Compact manifolds in hyperbolicity, Trans. Amer. Math. Soc., Tome 235 (1978), pp. 213-219 | MR 470252 | Zbl 0416.32013

[2] Buzzard, Gregery T.; Lu, Steven S.-Y. Double sections, dominating maps, and the Jacobian fibration, Amer. J. Math., Tome 122 (2000) no. 5, pp. 1061-1084 | Article | MR 1781932 | Zbl 0967.32015

[3] Campana, F Orbifoldes géométriques spéciales et classification biméromorphe des variétés kählériennes compactes (2008) (arxiv:0705.0737) | MR 2831280

[4] Dethloff, Gerd; Lu, Steven S.-Y. Logarithmic surfaces and hyperbolicity, Ann. Inst. Fourier (Grenoble), Tome 57 (2007) no. 5, pp. 1575-1610 | Article | Numdam | MR 2364143 | Zbl 1142.14024

[5] Faltings, G. Endlichkeitssätze für abelsche Varietäten über Zahlkörpern, Invent. Math., Tome 73 (1983) no. 3, pp. 349-366 | Article | MR 718935 | Zbl 0588.14026

[6] Hassett, Brendan; Tschinkel, Yuri Density of integral points on algebraic varieties, Rational points on algebraic varieties, Birkhäuser, Basel (Progr. Math.) Tome 199 (2001), pp. 169-197 | MR 1875174 | Zbl 1018.14008

[7] Kawamata, Yujiro Characterization of abelian varieties, Compositio Math., Tome 43 (1981) no. 2, pp. 253-276 | Numdam | MR 622451 | Zbl 0471.14022

[8] Kobayashi, Shoshichi Hyperbolic complex spaces, Springer-Verlag, Berlin, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], Tome 318 (1998) | MR 1635983 | Zbl 0917.32019

[9] Noguchi, Junjiro Lemma on logarithmic derivatives and holomorphic curves in algebraic varieties, Nagoya Math. J., Tome 83 (1981), pp. 213-233 | MR 632655 | Zbl 0429.32003

[10] Noguchi, Junjiro; Winkelmann, Jörg; Yamanoi, Katsutoshi Degeneracy of holomorphic curves into algebraic varieties, J. Math. Pures Appl. (9), Tome 88 (2007) no. 3, pp. 293-306 | MR 2355461 | Zbl 1135.32018

[11] Noguchi, Junjiro; Winkelmann, Jörg; Yamanoi, Katsutoshi The second main theorem for holomorphic curves into semi-abelian varieties. II, Forum Math., Tome 20 (2008) no. 3, pp. 469-503 | Article | MR 2418202 | Zbl 1145.32009

[12] Vojta, Paul Diophantine approximations and value distribution theory, Springer-Verlag, Berlin, Lecture Notes in Mathematics, Tome 1239 (1987) | MR 883451 | Zbl 0609.14011

[13] Vojta, Paul Integral points on subvarieties of semiabelian varieties. I, Invent. Math., Tome 126 (1996) no. 1, pp. 133-181 | Article | MR 1408559 | Zbl 1011.11040

[14] Vojta, Paul Integral points on subvarieties of semiabelian varieties. II, Amer. J. Math., Tome 121 (1999) no. 2, pp. 283-313 | Article | MR 1680329 | Zbl 1018.11027

[15] Winkelmann, Jörg On a special class of complex tori, J. Lie Theory, Tome 16 (2006) no. 1, pp. 93-95 | MR 2196416 | Zbl 1147.22007

[16] Winkelmann, Jörg On Brody and entire curves, Bull. Soc. Math. France, Tome 135 (2007) no. 1, pp. 25-46 | Numdam | MR 2430197 | Zbl 1159.32015