Nevanlinna theory for holomophic curves from annuli into semi-Abelian varieties
-
Si Duc Quang
Abstract
In this paper, we prove a lemma on logarithmic derivative for holomorphic curves from annuli into Kähler compact manifolds. As its application, a second main theorem for holomophic curves from annuli into semi-Abelian varieties intersecting with only one divisor is given.
This work was done during a stay of the author at Vietnam Institute for Advanced Study in Mathematics (VIASM). He would like to thank the institute for the support.
-
Communicated by Stanisława Kanas
References
[1] Griffiths, P.—King, J.: Nevanlinna theory and holomorphic mappings between algebraic varieties, Acta Math. 130 (1973), 145–220.10.1007/BF02392265Search in Google Scholar
[2] Khrystiyanyn, A. Y.—Kondratyuk, A. A.: On the Nevanlinna theory for meromorphic functions on annuli, I, Mat. Stud. 23(1) (2005), 19–30.Search in Google Scholar
[3] Khrystiyanyn, A. Y.—Kondratyuk, A. A.: On the Nevanlinna theory for meromorphic functions on annuli, II, Mat. Stud. 24(2) (2005), 57–68.Search in Google Scholar
[4] Lund, M.—Ye, Z.: Nevanlinna theory of meromorphic functions on annuli, Sci. China Math. 53 (2010), 547–554.10.1007/s11425-010-0037-3Search in Google Scholar
[5] Noguchi, J.—Ochiai, T.: Introduction to Geometric Function Theory in Several Complex Variables. Trans. Math. Monogr. 80, Amer. Math. Soc., Providence, Rhode Island, 1990.10.1090/mmono/080Search in Google Scholar
[6] Dethloff, G.—Lu, S. S. Y.: Logarithmic jet bundles and applications, Osaka J. Math. 38 (2001), 185–237.Search in Google Scholar
[7] Nevanlinna, R.: Einige Eideutigkeitssätze in der Theorie der meromorphen Funktionen, Acta Math. 48 (1926), 367–391.10.1007/BF02565342Search in Google Scholar
[8] Noguchi, J.: Lemma on logarithmic derivatives and holomorphic curves in algebraic varieties, Nagoya Math. J. 83 (1981), 213–233.10.1017/S0027763000019504Search in Google Scholar
[9] Noguchi, J.: Logarithmic jet spaces and extensions of Franchis’ theorem, Aspects Math. E9 (1986), 227–249.10.1007/978-3-663-06816-7_11Search in Google Scholar
[10] Noguchi, J.—Winkelmann, J.—Yamanoi, K.: The second main theorem for holomorphic curves into semi-Abelian varieties, Acta Math. 188 (2002), 129–161.10.1007/BF02392797Search in Google Scholar
[11] Quang, S. D.: Nevanlinna theory for holomorphic curves from punctured disks into semi-Abelian varieties, Intern. J. Math. 23(5) (2012), Art. ID 1250050.10.1142/S0129167X12500504Search in Google Scholar
[12] Weil, A.: Introduction à l’Étude des Variétés Kählériennes, Hermann, Paris, 1958.Search in Google Scholar
© 2022 Mathematical Institute Slovak Academy of Sciences
Articles in the same Issue
- Regular Papers
- Logical and algebraic properties of generalized orthomodular posets
- Integral prefilters and integral Eq-algebras
- Modules with fusion and implication based over distributive lattices: Representation and duality
- Localization of k × j-rough Heyting algebras
- Meet infinite distributivity for congruence lattices of direct sums of algebras
- Some exponential diophantine equations II: The equation x2 – Dy2 = kz for even k
- On extensions of the Open Door Lemma
- Nevanlinna theory for holomophic curves from annuli into semi-Abelian varieties
- Stability and feedback stabilizability of delay periodic differential equations with pairwise permutable matrix functions
- On the behaviour solutions of fractional and partial integro differential heat equations and its numerical solutions
- Oscillatory and asymptotic behavior of solutions of third-order quasi-linear neutral difference equations
- Some properties of Kantorovich variant of Chlodowsky-Szász operators induced by Boas-Buck type polynomials
- A Study on statistical versions of convergence of sequences of functions
- Fuzzy fixed point theorems and Ulam-Hyers stability of fuzzy set-valued maps
- Notes on affine Killing and two-Killing vector fields
- Prediction of the exponential fractional upper record-values
- On concomitants of generalized order statistics from generalized FGM family under a general setting
- One-parameter generalization of dual-hyperbolic Pell numbers
Articles in the same Issue
- Regular Papers
- Logical and algebraic properties of generalized orthomodular posets
- Integral prefilters and integral Eq-algebras
- Modules with fusion and implication based over distributive lattices: Representation and duality
- Localization of k × j-rough Heyting algebras
- Meet infinite distributivity for congruence lattices of direct sums of algebras
- Some exponential diophantine equations II: The equation x2 – Dy2 = kz for even k
- On extensions of the Open Door Lemma
- Nevanlinna theory for holomophic curves from annuli into semi-Abelian varieties
- Stability and feedback stabilizability of delay periodic differential equations with pairwise permutable matrix functions
- On the behaviour solutions of fractional and partial integro differential heat equations and its numerical solutions
- Oscillatory and asymptotic behavior of solutions of third-order quasi-linear neutral difference equations
- Some properties of Kantorovich variant of Chlodowsky-Szász operators induced by Boas-Buck type polynomials
- A Study on statistical versions of convergence of sequences of functions
- Fuzzy fixed point theorems and Ulam-Hyers stability of fuzzy set-valued maps
- Notes on affine Killing and two-Killing vector fields
- Prediction of the exponential fractional upper record-values
- On concomitants of generalized order statistics from generalized FGM family under a general setting
- One-parameter generalization of dual-hyperbolic Pell numbers
