Meromorphic maps from ${\Bbb C}^{p}$ into semi-abelian varieties and general projective varieties

Abstract

In 1974, W. Stoll proposed a method of studying holomorphic functions of several complex variables by reducing them to one variable through fiber integration. In this paper, we use this method to extend some important Nevanlinna-type results for holomorphic curves into projective varieties to meromorphic maps from ${\Bbb C}^{p}$ to projective varieties. This includes Bloch's theorem and Noguchi-Winkelmann-Yamanoi's Second Main Theorem for holomorphic maps into semi-abelian varieties intersecting an effective divisor, as well as Huynh-Vu-Xie's Second Main Theorem for meromorphic maps into projective space intersecting with a generic hypersurface with sufficiently high degree.