A note on positivity of the CM line bundle
A note on positivity of the CM line bundle
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关于 CM 线束积极性的说明
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
J. Ross
中科院分区：
文献类型：
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作者：
J. Fine;J. Ross
我们表明，积极的CM线与一个家庭的极化品种是密切相关的稳定性，其成员。我们证明了CM线是nef的任何曲线，满足稳定的轨迹，它是伪有效的（即在封闭的有效锥），只要有至少一个稳定的纤维。我们给出的例子表明，CM线可以是严格负的或严格正的曲线在不稳定的轨迹。
We show that positivity of the CM line associated to a family of polarised varieties is intimately related to the stability of its members. We prove that the CM line is nef on any curve which meets the stable locus, and that it is pseudoeffective (i.e. in the closure of the effective cone) as long as there is at least one stable fibre. We give examples showing that the CM line can be strictly negative or strictly positive on curves in the unstable locus.