Duval, Julien Singularities of Ahlfors currents. (Singularités des courants d’Ahlfors.) (French. English summary) Zbl 1243.32012 Ann. Sci. Éc. Norm. Supér. (4) 39, No. 3, 527-533 (2006). Summary: We prove that an algebraic curve charged by a current coming from an entire curve is rational or elliptic. This answers a question by M. Păun. Cited in 6 Documents MSC: 32H30 Value distribution theory in higher dimensions 32C30 Integration on analytic sets and spaces, currents 32H25 Picard-type theorems and generalizations for several complex variables 32U40 Currents PDF BibTeX XML Cite \textit{J. Duval}, Ann. Sci. Éc. Norm. Supér. (4) 39, No. 3, 527--533 (2006; Zbl 1243.32012) Full Text: DOI Numdam EuDML OpenURL References: [1] Brunella M. , Courbes entières et feuilletages holomorphes , Ens. Math. 45 ( 1999 ) 195 - 216 . MR 1703368 | Zbl 1004.32011 · Zbl 1004.32011 [2] Demailly J.-P. , Monge-Ampère operators, Lelong numbers and intersection theory , in: Complex Analysis and Geometry , Univ. Ser. Math. , Plenum , New York , 1993 , pp. 115 - 193 . MR 1211880 | Zbl 0792.32006 · Zbl 0792.32006 [3] Dujardin R. , Laminar currents and dynamics I: Structure properties of laminar currents on \({P}^{2}\) , math.CV/0403292 . arXiv · Zbl 1076.37033 [4] McQuillan M. , Diophantine approximations and foliations , Publ. Math. IHÉS 87 ( 1998 ) 121 - 174 . Numdam | MR 1659270 | Zbl 1006.32020 · Zbl 1006.32020 [5] Morgan F. , Geometric Measure Theory. A Beginner’s Guide , Academic Press , San Diego , 2000 . MR 1775760 | Zbl 0974.49025 · Zbl 0974.49025 [6] Nevanlinna R. , Analytic Functions , Grund. Math. Wiss. , vol. 162 , Springer , Berlin , 1970 . MR 279280 | Zbl 0199.12501 · Zbl 0199.12501 [7] Nishino T. , Suzuki M. , Sur les singularités essentielles et isolées des applications holomorphes à valeurs dans une surface complexe , Publ. RIMS Kyoto 16 ( 1980 ) 461 - 497 . Article | MR 594913 | Zbl 0506.32007 · Zbl 0506.32007 [8] Paun M. , Currents associated to transcendental entire curves on compact Kähler manifolds, Preprint , 2003. [9] Sikorav J.-C. , Some properties of holomorphic curves in almost complex manifolds , in: Holomorphic Curves in Symplectic Geometry , Progr. Math. , vol. 117 , Birkhäuser , Basel , 1994 , pp. 165 - 189 . MR 1274929 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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.