On a notion of speciality of linear systems in P^n
On a notion of speciality of linear systems in P^n
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论P^n中线性系统的特殊性概念
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
Elisa Postinghel
中科院分区：
文献类型：
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作者：
M. Brambilla;Olivia Dumitrescu;Elisa Postinghel
给定P^n中具有指定多个通用点的线性系统，通过其线性基轨迹的爆破，计算其严格变换的上同调群。这导致我们给出了一个新的线性系统期望维度的定义，它考虑了线性基轨迹的贡献，并由此引入了线性特性的概念。我们研究了这样一个概念，给出了线性系统对任意点数线性非特殊的充分条件和点数较少的必要条件。
Given a linear system in P^n with assigned multiple general points we compute the cohomology groups of its strict transforms via the blow-up of its linear base locus. This leads us to give a new definition of expected dimension of a linear system, which takes into account the contribution of the linear base locus, and thus to introduce the notion of linear speciality. We investigate such a notion giving sufficient conditions for a linear system to be linearly non-special for arbitrary number of points, and necessary conditions for small numbers of points.