Second main theorem for meromorphic mappings with moving hypersurfaces in subgeneral position

Abstract

Let $f$ be an algebraically nondegenerate meromorphic mapping from ${\mathbb{C}}^m$ into ${\mathbb{P}}^n(\mathbb{C})$ and let $Q_1,...,Q_q$ be $q$ hypersurfaces in ${\mathbb{P}}^n(\mathbb{C})$ of degree $d_i$, in $N-$subgeneral position. In this paper, we will prove that, for every $\epsilon >0$, there exists a positive integer $M$ such that $$||(q-(N-n+1)(n+1)-\epsilon )T_f(r)\le \sum _{i=1}^q\frac{1}{d_i}{N}^{[M]}(r,f^{\ast }{Q}_i)+o(T_f(r)).$$ Moreover, an explicit estimate for $M$ is given. Our result is an extension of the previous second main theorem for the mappings and moving hyperplanes or moving hypersurfaces.

21 pages. arXiv admin note: text overlap with arXiv:1610.03951

References in corpus (1)

• Degeneracy second main theorems for meromorphic mappings into projective varieties with hypersurfaces

Cited by in corpus (4)

• Meromorphic mappings into projective varieties with arbitrary families of moving hypersurfaces
• Non-integrated defect relation for meromorphic maps from a Kähler manifold intersecting hypersurfaces in subgeneral of ${\mathbb{P}}^n(\mathbb{C})$
• Second main theorem for holomorphic curves into algebraic varieties intersecting moving hypersurfaces targets
• Holomorphic maps from complex discs intersecting families of hypersurfaces