The cone of effective one—cycles of certain G —varieties
The cone of effective one—cycles of certain G —varieties
复制标题
某些 G 品种的有效单循环锥体
DOI：
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发表时间：
2002
期刊：
影响因子：
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通讯作者：
M. Brion
中科院分区：
文献类型：
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作者：
M. Brion
设X是允许具有唯一闭轨道的半单群作用的正规射影变。我们在X上构造有限多条有理曲线，所有曲线都有一个公点，使得X上的每一个有效单循环都合理地等价于这些曲线的非负有理系数的唯一线性组合。当X为非奇异时，这些曲线为射影线，它们生成一环的整Chow群。
Let X be a normal projective variety admitting an action of a semisimple group with a unique closed orbit. We construct finitely many rational curves in X, all having a common point, such that every effective one—cycle on X is rationally equivalent to a unique linear combination of these curves with non-negative rational coefficients. When X is nonsingular, these curves are projective lines, and they generate the integral Chow group of one—cycles.