Lemma on logarithmic derivatives and holomorphic curves in algebraic varieties

DOI10.1017/S0027763000019504zbMath0429.32003OpenAlexW1496575983WikidataQ124815402 ScholiaQ124815402MaRDI QIDQ3866387

Junjiro Noguchi

Publication date: 1981

Published in: Nagoya Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0027763000019504

zbMATH Keywords

holomorphic curvequasi-Abelian varietysurface of general typeextension theorem for holomorphic curveslemma on logarithmic derivatives

Mathematics Subject Classification ID

Continuation of analytic objects in several complex variables (32D15) Nevanlinna theory; growth estimates; other inequalities of several complex variables (32A22) Value distribution theory in higher dimensions (32H30) Transcendental methods of algebraic geometry (complex-analytic aspects) (32J25)

Related Items (26)

Nevanlinna theory for holomophic curves from annuli into semi-abelian varieties ⋮ NEVANLINNA THEORY FOR HOLOMORPHIC CURVES FROM PUNCTURED DISKS INTO SEMI-ABELIAN VARIETIES ⋮ Big Picard theorem for meromorphic mappings with moving hyperplanes in \(\mathbf{P}^n(\mathbf{C})\) ⋮ Degeneracy of holomorphic curves into algebraic varieties ⋮ A short analytic proof of closedness of logarithmic forms ⋮ Algebro-geometric version of Nevanlinna’s lemma on logarithmic derivative and applications ⋮ The second Main theorem for meromorphic mappings into a complex projective space ⋮ Picard theorem for holomorphic curves from a punctured disc into \(\mathbb{P}^n(\mathbb{C})\) with few hypersurfaces in subgeneral position ⋮ Extension of holomorphic mappings for several moving hypersurfaces ⋮ On the positivity of the logarithmic cotangent bundle ⋮ Degeneracy of entire curves in log surfaces with \(\bar q = 2\) ⋮ Integral points of bounded degree on affine curves ⋮ A new unicity theorem and Erdös' problem for polarized semi-abelian varieties ⋮ Analytic Ax-Schanuel for semi-abelian varieties and Nevanlinna theory ⋮ A difference Picard theorem for meromorphic functions of several variables ⋮ On a quaternionic Picard theorem ⋮ Generalization of uniqueness theorem for meromorphic mappings sharing hyperplanes ⋮ Nevanlinna theory and Diophantine approximation ⋮ Logarithmic surfaces and hyperbolicity ⋮ Value distribution of meromorphic mappings into compactified locally symmetric spaces ⋮ Unnamed Item ⋮ Degeneracy of holomorphic curves into algebraic varieties. II ⋮ Curves in quadric and cubic surfaces whose complements are Kobayashi hyperbolically imbedded ⋮ Generalizations of Siegel's and Picard's theorems ⋮ Recent results on the Kobayashi and Green-Griffiths-Lang conjectures ⋮ The second main theorem for holomorphic curves into semi-Abelian varieties

Cites Work

• On Bloch's conjecture
• The lemma of the logarithmic derivative in several complex variables
• On holomorphic curves in algebraic varieties with ample irregularity
• On meromorphic maps into the complex projective space
• Hermitesche Metriken und normale Familien holomorpher Abbildungen
• Extensions of the big Picard's theorem
• Families of holomorphic maps into the projective space omitting some hyperplanes
• Nevanlinna theory and holomorphic mappings between algebraic varieties
• Some Picard Theorems for Holomorphic Maps to Algebraic Varieties
• Intrinsic distances, measures and geometric function theory

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