Second Main Theorems for Holomorphic Curves in the Projective Space with Slowly Moving Hypersurfaces

Let f:C -> PN(C)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f : {\mathbb C} \rightarrow {{\mathbb P}<^>{N}}({\mathbb C})$$\end{document} be a nonconstant holomorphic curve and Kf\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\cal K}_{f}$$\end{document} be the subfield of meromorphic function field on & Copf; consisting of all meromorphic functions of slow growth with respect to f. Let D1,& mldr;,Dq be slowly moving hypersurfaces defined by homogeneous polynomials in Kf[x0,& mldr;,xN]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\cal K}_{f}[x_{0},\ldots,x_{N}]$$\end{document}. In this paper, the second main theorems for nonconstant holomorphic curve f and slowly moving hypersurfaces D1,& mldr;,Dq with respect to f are given. The motivation comes from the replacing hypersurfaces technique posed by Si Duc Quang and Nochka weights method.