无对数A-超几何级数
Logarithm-free A-hypergeometric series
摘要：
给出了A-超几何（或GKZ超几何）系统的无量纲级数解空间的维数公式。在A张成的凸包是单形的情况下，给出了系统的秩公式，刻画了例外集，证明了A定义的复曲面簇的Cohen-Macaulay性与例外集的空性的等价性.此外，我们把A-超几何系统分类为解析D-模。
英文摘要：
We give a dimension formula for the space of logarithm-free series solutions to an A-hypergeometric (or a GKZ hypergeometric) system. In the case where the convex hull spanned by A is a simplex, we give a rank formula for the system, characterize the exceptional set, and prove the equivalence of the Cohen-Macaulayness of the toric variety defined by A with the emptiness of the exceptional set. Furthermore we classify A-hypergeometric systems as analytic D-modules.
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