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arXiv · 1610.09198

A non-integrated hypersurface defect relation for meromorphic maps over complete K\"ahler manifolds into projective algebraic varieties

Wei Chen·Qi Han
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Abstract

In this paper, a non-integrated defect relation for meromorphic maps from complete K\"ahler manifolds $M$ into smooth projective algebraic varieties $V$ intersecting hypersurfaces located in $k$-subgeneral position 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 $k$, $\dim_{\,\mathbb{C}}(V)$ and the degrees of the hypersurfaces considered. In addition, this defect relation recovers Hirotaka Fujimoto [Theorem 1.1; MR0884636 (88m:32049); Japan. J. Math. (N.S.) 11 (1985), no. 2, 233-264.] when subjected to the same conditions.

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Wei Chen, Qi Han. 2016-10-28. A non-integrated hypersurface defect relation for meromorphic maps over complete K\"ahler manifolds into projective algebraic varieties. https://doi.org/10.2996/kmj/1530496842

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