发表机构
Capital Normal University（首都师范大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究证明了A-超几何系统特征标圈重数的上半连续性，证实了Schulze与Walther的猜想，还构造了特定半群环揭示Gevrey跳跃轨迹的性质。
AI 中文摘要
我们证明，对每个有理射影权重，A-超几何系统的特征标圈重数在参数中是上半连续的，从而证明了Schulze与Walther提出的猜想[Duke Math. J. 142 (2008), 465--509]。该证明利用了满足固定乘积支撑条件的滤过族的 specialization 公式，将特殊与一般特征标圈的差表示为第一个Tor模的特征标圈。结合Gevrey指标定理，这得到了一般Gevrey不规则性及其每个分次维数的上半连续性。我们还构造了非Cohen-Macaulay半群环，其Gevrey维数在参数中保持恒定，尽管存在真实的不规则斜率，这表明Gevrey跳跃轨迹不必与由Ext定义的完整例外排列重合。
英文摘要
We show that the characteristic cycle multiplicities of $A$-hypergeometric systems are upper semicontinuous in the parameter for every rational projective weight, thereby proving a conjecture of Schulze and Walther [Duke Math. J. 142 (2008), 465--509]. The proof uses a specialization formula for filtered families satisfying a fixed product support condition, expressing the difference between the special and generic characteristic cycles as the characteristic cycle of the first Tor module. Combined with the Gevrey index theorem, this yields upper semicontinuity of generic Gevrey irregularity and of each of its graded dimensions. We also construct non-Cohen--Macaulay semigroup rings whose Gevrey dimensions are constant in the parameter despite the presence of a genuine irregular slope, showing that the Gevrey jump locus need not coincide with the full exceptional arrangement defined by Ext.
Comments26 pages
