Toric vector bundles, branched covers of fans, and the resolution property
Toric vector bundles, branched covers of fans, and the resolution property
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环面矢量丛、扇形分支覆盖层和分辨率属性
DOI：
10.1090/s1056-3911-08-00485-2
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发表时间：
2006
影响因子：
1.8
通讯作者：
S. Payne
中科院分区：
文献类型：
--
作者：
S. Payne
我们将复曲面簇X（X）上的每个复曲面向量丛与扇复曲面的“分支覆盖”以及分支覆盖上的分段线性函数相关联。这种构造推广了复曲面卡地亚因子和分段线性函数之间的通常对应关系。我们应用这种组合几何技术来研究向量丛相干层的决议的存在性，使用奇异nonquasiprojective环面三倍作为试验场。我们的主要新成果是建设完整的复曲面threefolds没有非平凡的复曲面向量丛的秩小于或等于三。组合几何部分的文件，其中发展的理论锥复合体及其分支覆盖，可以独立阅读。
We associate to each toric vector bundle on a toric variety X(∆) a “branched cover” of the fan ∆ together with a piecewise-linear function on the branched cover. This construction generalizes the usual correspondence between toric Cartier divisors and piecewise-linear functions. We apply this combinatorial geometric technique to investigate the existence of resolutions of coherent sheaves by vector bundles, using singular nonquasiprojective toric threefolds as a testing ground. Our main new result is the construction of complete toric threefolds that have no nontrivial toric vector bundles of rank less than or equal to three. The combinatorial geometric sections of the paper, which develop a theory of cone complexes and their branched covers, can be read independently.