An Extension of the Cartan–nochka Second Main Theorem for Hypersurfaces

Dethloff, Gerd; Tan, Tran Van; Thai, Do Duc

doi:10.1142/s0129167x11007070

Cited by 5 publications

(1 citation statement)

References 18 publications

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“…Ru and Sogome [17] (see also Yan [20]), and Tan and Truong [19] generalized independently the preceding Theorem 1.1 in the way that P n (C) is replaced by a projective algebraic variety V ⊆ P N (C) and hyperplanes in P n (C) located in general position are extended to hypersurfaces in P N (C) located in different types of k-subgeneral positions. One recalls that the k-subgeneral position condition used in [19] comes from Dethloff, Tan and Thai [3,Definition 1.1].…”

Section: Introductionmentioning

confidence: 99%

A non-integrated hypersurface defect relation for meromorphic maps over complete Kähler manifolds into projective algebraic varieties

Chen¹,

Han²

2018

Kodai Math. J.

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In this paper, a non-integrated defect relation for meromorphic maps from complete Kähler manifolds M into smooth projective algebraic varieties V intersecting hypersurfaces located in k-subgeneral position (see (1.5) below) is proved. The novelty of this result lies in that both the upper bound and the truncation level of our defect relation depend only on k, dim C (V ) and the degrees of the hypersurfaces considered; besides, this defect relation recovers Hirotaka Fujimoto [6, Theorem 1.1] when subjected to the same condition. Now, the original result of Fujimoto [6, Theorem 1.1] can be stated as follows.

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