三维光滑复射影簇上全纯曲线的退化性

Degeneracy of Holomorphic Curves on Threefolds

讨论三维光滑复射影簇X上全纯曲线f:C→X的退化性.设D_1…,D_r为X上处于一般位置的相异的不可约有效除子.假定D_1…,D_r均为nef除子,而且存在正整数n_1…,n_r,c,使得n_in_jn_k(D_i.D_j.D_k)=c对所有i,j,k均成立.如果f的像取不到D_1…,D_r上的点,那么只要r≥11,f必定代数退化,即它的像包含于X的某个代数真子集中.

We consider the degeneracy of holomorphic curve f from C to a complex nonsingular projective variety X of dimension 3. Let D1,..., Dr be distinct irreducible effective and nef divisors on X located in general position. Assume that there exist positive integers nl , nr, c, such that ninjnk（Di.Dj.Dk） = c for any i, j, k. If r≥ 11 and the image of f omits D1,…,Dr, then f is algebraically degenerate, i.e., its image is contained in a proper algebraic subset of X.