On the length of an extremal rational curve
On the length of an extremal rational curve
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关于极值有理曲线的长度
DOI：
10.1007/bf01232281
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发表时间：
1991
影响因子：
3.1
通讯作者：
Y. Kawamata
中科院分区：
文献类型：
--
作者：
Y. Kawamata
定理1设g：X~ Y是特征为零的域上的代数簇的投射态射，A是X上的Q-因子，使得（X，A）对只有对数终端奇点。设E是退化轨迹Exc（g）的不可约分支，={x~ X; g在x上不是同构}，n= dimE-dimg（E）.假设-（Kx+ A）是g-样本。则E被有理曲线族{L2}~覆盖。ea使得g（L2）是点，并且（-（Kx+ d）. La）
Theorem 1 Let g: X~ Y be a projective morphism of algebraic varieties over a field of characteristic zero, and A a Q-divisor on X such that the pair (X, A) has only log-terminal singularities. Let E be an irreducible component of the degenerate locus Exc (g),={x~ X; g is not an isomorphism at x}, and let n= dimE--dimg (E). Assume that-(Kx+ A) is g-ample. Then E is covered by a family of rational curves {L2}~. ea such that the g (L2) are points and that (-(Kx+ d). La)