Positivity for toric vector bundles
Positivity for toric vector bundles
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复曲面向量束的正性
DOI：
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
S. Payne
中科院分区：
文献类型：
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作者：
M. Hering;M. Mustaţă;S. Payne
我们分别证明了完全环变上的等变向量束当且仅当其对每条不变曲线的约束为内充裕时是内充裕的。进一步，我们证明了网络矢量束在每一点上都有一个不消失的全局截面，并推导出底层矢量束是平凡的当且仅当其对每条不变曲线的约束是平凡的。我们应用我们的方法和结果，特别地研究了当L是一个充足的线束时，在L的截面上作为评价映射核的向量束M_L。我们给出了这样的bundle的扭曲的例子，它们是充足的，但不是全局生成的。
We show that an equivariant vector bundle on a complete toric variety is nef or ample if and only if its restriction to every invariant curve is nef or ample, respectively. Furthermore, we show that nef toric vector bundles have a nonvanishing global section at every point, and deduce that the underlying vector bundle is trivial if and only if its restriction to every invariant curve is trivial. We apply our methods and results to study, in particular, the vector bundles M_L that arise as the kernel of the evaluation map on sections of L, when L is an ample line bundle. We give examples of twists of such bundles that are ample but not globally generated.