Winkelmann, Jörg Degeneracy of entire curves in log surfaces with \(\bar q = 2\). (English. French summary) Zbl 1250.32016 Ann. Inst. Fourier 61, No. 4, 1517-1537 (2011). The author determines those algebraic surfaces that admit non-degenerate entire curves. The results involve the logarithmic irregularity, the logarithmic Kodaira dimension, and the quasi Albanese map. Many interesting examples are given. Reviewer: Ingo Lieb (Bonn) Cited in 1 ReviewCited in 1 Document MSC: 32H25 Picard-type theorems and generalizations for several complex variables 32H30 Value distribution theory in higher dimensions Keywords:entire curve; algebraic suface; logarithmic irregularity PDFBibTeX XMLCite \textit{J. Winkelmann}, Ann. Inst. Fourier 61, No. 4, 1517--1537 (2011; Zbl 1250.32016) Full Text: DOI EuDML References: [1] Brody, Robert, Compact manifolds in hyperbolicity, Trans. Amer. Math. Soc., 235, 213-219 (1978) · Zbl 0416.32013 [2] Buzzard, Gregery T.; Lu, Steven S.-Y., Double sections, dominating maps, and the Jacobian fibration, Amer. J. Math., 122, 5, 1061-1084 (2000) · Zbl 0967.32015 [3] Campana, F., Orbifoldes géométriques spéciales et classification biméromorphe des variétés kählériennes compactes (2008) · Zbl 1236.14039 [4] Dethloff, Gerd; Lu, Steven S.-Y., Logarithmic surfaces and hyperbolicity, Ann. Inst. Fourier (Grenoble), 57, 5, 1575-1610 (2007) · Zbl 1142.14024 [5] Faltings, G., Endlichkeitssätze für abelsche Varietäten über Zahlkörpern, Invent. Math., 73, 3, 349-366 (1983) · Zbl 0588.14026 [6] Hassett, Brendan; Tschinkel, Yuri, Rational points on algebraic varieties, 199, 169-197 (2001) · Zbl 1018.14008 [7] Kawamata, Yujiro, Characterization of abelian varieties, Compositio Math., 43, 2, 253-276 (1981) · Zbl 0471.14022 [8] Kobayashi, Shoshichi, Hyperbolic complex spaces, 318 (1998) · Zbl 0917.32019 [9] Noguchi, Junjiro, Lemma on logarithmic derivatives and holomorphic curves in algebraic varieties, Nagoya Math. J., 83, 213-233 (1981) · Zbl 0429.32003 [10] Noguchi, Junjiro; Winkelmann, Jörg; Yamanoi, Katsutoshi, Degeneracy of holomorphic curves into algebraic varieties, J. Math. Pures Appl. (9), 88, 3, 293-306 (2007) · Zbl 1135.32018 [11] Noguchi, Junjiro; Winkelmann, Jörg; Yamanoi, Katsutoshi, The second main theorem for holomorphic curves into semi-abelian varieties. II, Forum Math., 20, 3, 469-503 (2008) · Zbl 1145.32009 [12] Vojta, Paul, Diophantine approximations and value distribution theory, 1239 (1987) · Zbl 0609.14011 [13] Vojta, Paul, Integral points on subvarieties of semiabelian varieties. I, Invent. Math., 126, 1, 133-181 (1996) · Zbl 1011.11040 [14] Vojta, Paul, Integral points on subvarieties of semiabelian varieties. II, Amer. J. Math., 121, 2, 283-313 (1999) · Zbl 1018.11027 [15] Winkelmann, Jörg, On a special class of complex tori, J. Lie Theory, 16, 1, 93-95 (2006) · Zbl 1147.22007 [16] Winkelmann, Jörg, On Brody and entire curves, Bull. Soc. Math. France, 135, 1, 25-46 (2007) · Zbl 1159.32015 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.