We investigate the solution space to certain [Formula: see text]-hypergeometric [Formula: see text]-modules, which were defined and studied by Gelfand, Kapranov, and Zelevinsky. We show that the solution space can be identified with certain relative cohomology group of the toric variety determined by [Formula: see text], which generalizes the results of Huang, Lian, Yau and Zhu. As a corollary, we also prove the existence of rank one points for complete intersections in toric varieties.

中文翻译：

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A-超几何系统和相对上同调

我们研究了某些 [公式：见文本]-超几何 [公式：见文本]-模块的解空间，这些模块由 Gelfand、Kapranov 和 Zelevinsky 定义和研究。我们证明了解空间可以识别为由[公式：见正文]确定的复曲面簇的某个相对上同调群，它概括了黄、连、丘和朱的结果。作为推论，我们还证明了复曲面变体中完全交集的秩一点的存在。