Fukuoka Complex Analysis Seminar

Let {D_i} be n+1 hypersurfaces in P^n with total degree >=n+2, in general position and satisfies a generic geometric condition: every n hypersurfaces intersect only at smooth points and the intersection is transversal. Then, for every algebraically nondegenerate entire holomorphic curve f:C->P^n, we show a Second Main Theorem: sum \delta(f,D_i)<n+1 in terms of defect inequality in Nevanlinna theory. This is the first result in the literature on Second Main Theorem for n+1 general hypersurfaces in P^n with optimal total degrees. This is a joint work with Dinh Tuan Huynh, Ruiran Sun and Song-Yan Xie.