Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 42, 2017, 979-996

THE SECOND MAIN THEOREM FOR HOLOMORPHIC CURVES INTERSECTING HYPERSURFACES WITH CASORATI DETERMINANT INTO COMPLEX PROJECTIVE SPACES

Tingbin Cao and Jun Nie

Nanchang University, Department of Mathematics
Nanchang, 330031, P.R. China; tbcao 'at' ncu.edu.cn

Nanchang University, Department of Mathematics
Nanchang, 330031, P.R. China; jniemath 'at' 126.com

Abstract. {\footnotesize{\textbf{Abstract.} Let f : C → Pⁿ(C) be a holomorphic curves with hyperorder strictly less than 1, and algebraically nondegenerate over the field P_c¹ which consists of c-periodic meromorphic functions on C. Let {Q_j}_j=1^q be fixed or c-periodic slowly moving hypersurfaces with degree d_j (j ∈ {1,...,q}) in (weakly) N-subgeneral position in Pⁿ(C). In this paper, we prove a difference version of the second main theorem for f intersecting {Q_j}_j=1^q by using the Casorati determinant. A difference counterpart of the truncated second main theorem is also obtained. Our results extend the second main theorems for differences with fixed hyperplanes [9] or c-periodic slowly moving hyperplanes [10].

2010 Mathematics Subject Classification: Primary 32H30; Secondary 30D35.

Key words: Holomorphic curve, hypersurfaces, second main theorem, complex projective space, Casorati determinant.

Reference to this article: T. Cao and J. Nie: The second main theorem for holomorphic curves intersecting hypersurfaces with Casorati determinant into complex projective spaces. Ann. Acad. Sci. Fenn. Math. 42 (2017), 979-996.

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https://doi.org/10.5186/aasfm.2017.4259