Gromov-Witten theory and invariants of matroids
Gromov-Witten theory and invariants of matroids
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Gromov-Witten 理论和拟阵不变量
DOI：
10.1007/s00029-022-00780-4
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发表时间：
2022
期刊：
影响因子：
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通讯作者：
Ranganathan D
中科院分区：
文献类型：
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作者：
Ranganathan D
我们使用的技术从Gromov-Witten理论构造新的不变量拟阵采取值的Chow群的空间中的有理曲线的permutohedral复曲面品种。当拟阵是可实现的一个复杂的超平面安排，我们的不变量符合虚拟的基本类用于定义对数Gromov-Witten理论的美妙模型的安排补充，任何对数结构上支持的美妙的边界。当边界为空时，这意味着超平面排列的奇妙模型的量子上同调环是组合不变量，即，它只依赖于拟阵当边界因子是最大的，我们使用环面交理论转换的虚拟基本类到一个平衡的加权风扇在向量空间中，具有预期的维数。我们解释了如何相关的Gromov-Witten理论是完全编码的交叉与此加权风扇。我们包括一些问题，其积极的答案将导致一个定义良好的Gromov-Witten理论的不可实现拟阵。
We use techniques from Gromov–Witten theory to construct new invariants of matroids taking value in the Chow groups of spaces of rational curves in the permutohedral toric variety. When the matroid is realizable by a complex hyperplane arrangement, our invariants coincide with virtual fundamental classes used to define the logarithmic Gromov–Witten theory of wonderful models of arrangement complements, for any logarithmic structure supported on the wonderful boundary. When the boundary is empty, this implies that the quantum cohomology ring of a hyperplane arrangement’s wonderful model is a combinatorial invariant, i.e., it depends only on the matroid. When the boundary divisor is maximal, we use toric intersection theory to convert the virtual fundamental class into a balanced weighted fan in a vector space, having the expected dimension. We explain how the associated Gromov–Witten theory is completely encoded by intersections with this weighted fan. We include a number of questions whose positive answers would lead to a well-defined Gromov–Witten theory of non-realizable matroids.