摘要翻译：
我们分别证明了完备toric簇上的等变向量丛是nef或ample的当且仅当它对每条不变曲线的限制是nef或ample的。进一步，我们证明了nef多环向量丛在每个点上都有一个非消失的整体截面，并推导了下向量丛是平凡的当且仅当它对每条不变曲线的限制是平凡的。我们应用我们的方法和结果，特别研究了当L是一个充足的线丛时，在L的截面上作为求值映射的核而出现的向量丛M_L。我们给出了这样的束的扭曲的例子，这些束是充足的，但不是全局产生的。
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英文标题：
《Positivity for toric vector bundles》
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作者：
Milena Hering, Mircea Mustata, and Sam Payne
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最新提交年份：
2009
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分类信息：

一级分类：Mathematics        数学
二级分类：Algebraic Geometry        代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
  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.
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PDF链接：
https://arxiv.org/pdf/0805.4035