The Second Main Theorem for Hypersurfaces

Abstract

Abstract. The purpose of this article is twofold. The first is to show the Second Main Theorem for degenerate holomorphic curves into P n (C) with hypersurface targets located in n-subgeneral position. The second is to show the Second Main Theorem with truncated counting functions for nondegenerate holomorphic curves into P n (C) with hypersurface targets in general position. Finally, by applying the above result, a unicity theorem for algebraically nondegenerate curves into P 2 (C) with hypersurface targets in general position is also given.

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

“…For the case where hypersurfaces are not in general position, in [21] Thai and Thu obtained a Second Main Theorem for algebraically non-degenerate holomorphic maps f : C → CP k ⊂ CP n , without truncated multiplicities, and for a special class of hypersurfaces in CP n . In 2009, Ru [17] proved that …”

“…Recently, the Second Main Theorem for the case of hypersurfaces in general position was established by Ru ([16], [17]), see also Dethloff and Tan [5]. For the case where hypersurfaces are not in general position, in [21] Thai and Thu obtained a Second Main Theorem for algebraically non-degenerate holomorphic maps f : C → CP k ⊂ CP n , without truncated multiplicities, and for a special class of hypersurfaces in CP n .…”