三维光滑复射影簇上全纯曲线的退化性

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.

Degeneracy of Holomorphic Curves on Threefolds

We consider thedegeneracy of holomorphic curve $f$ from $mathbb{C}$ to a complexnonsingular projective variety $X$ of dimension 3. Let$D_1,ldots,D_r$ be distinct irreducible effective and nefdivisors on $X$ located in general position. Assume that thereexist positive integers $n_1,ldots,n_r,c$, such that$n_in_jn_k(D_i.D_j.D_k)=c$ for any $i,j,k$. If $rge 11$ and theimage of $f$ omits $D_1,ldots,D_r$, then $f$ is algebraicallydegenerate, i.e., its image is contained in a proper algebraicsubset of $X$.