AI 中文总结
本文研究A超几何级数的希尔伯特级数与对数次数，构造了负支链Stanley–Reisner环的Artinian商，得到局部伪指标理想正交补等的分次维数，无需Cohen–Macaulay假设，特殊情况可化为链的h多项式。
AI 中文摘要
给定齐次A超几何系统的一个通用权向量和一个伪指数，利用所有对应的标准对（包括嵌入的标准对），我们构造了负支链的Stanley–Reisner环的一个Artinian商。其希尔伯特级数给出了局部伪指标理想正交补的分次维数，且在Okuyama–Saito Frobenius条件下，给出了实际级数解的首项对数系数空间的分次维数。该构造无需Cohen–Macaulay假设。当出现一个顶维标准对且该链为Cohen–Macaulay时，希尔伯特级数会专门化为该链的h多项式。
英文摘要
Fix a generic weight vector and a fake exponent of a homogeneous $A$-hypergeometric system. Using all corresponding standard pairs, including embedded ones, we construct an Artinian quotient of the Stanley--Reisner ring of the link of the negative support. Its Hilbert series gives the graded dimensions of the orthogonal complement of the local fake indicial ideal and, under the Okuyama--Saito Frobenius condition, those of the leading logarithmic coefficient space of actual series solutions. The construction requires no Cohen--Macaulay hypothesis. When a top-dimensional standard pair occurs and the link is Cohen--Macaulay, the Hilbert series specializes to the $h$-polynomial of the link.
Comments23 pages
