A超几何系统欧拉纤维上的有限方向系数模块
Finite Directional Coefficient Modules over Euler Fibers of $A$-Hypergeometric Systems
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中文总结 AI 辅助
该研究针对A超几何系统欧拉纤维，在不附加齐次性等条件下，分析定向形式对数解，证明有限个指数格贡献非零解空间，建立Macaulay逆系统对偶关系并给出相关实现准则。
中文摘要 AI 辅助
设A为满秩整数矩阵，β为复参数，考虑与之关联的A超几何系统。在不假设齐次性、尖点性或正性的前提下，我们研究欧拉纤维中所有指数格上的定向形式对数解。对于固定的格通用方向，负支撑层由有理符号多面体描述，归一化将每个指数格上的系数方程简化为有限方向系数模块。我们证明仅有限个指数格贡献非零定向解空间，且所有贡献的系数模块均具有有限长度。Macaulay逆系统对偶将全格解空间的维数与对应全格模块的长度等同，我们还给出了显式形式级数实现及所有可实现最低指数的多项式冒理想准则。
英文摘要
Let \(A\) be a full-rank integer matrix, let \(β\) be a complex parameter, and consider the associated \(A\)-hypergeometric system. Without assuming homogeneity, pointedness, or positivity, we study directed formal logarithmic solutions over all exponent lattices in the Euler fiber. For a fixed lattice-generic direction, negative-support strata are described by rational sign polyhedra, and normalization reduces the coefficient equations on each exponent lattice to a finite directional coefficient module. We prove that only finitely many exponent lattices contribute nonzero directed solution spaces and that all contributing coefficient modules have finite length. Macaulay inverse-system duality identifies the dimension of the all-lattice solution space with the length of the corresponding all-lattice module. We also give an explicit formal-series realization and a polynomial colon-ideal criterion for all realizable lowest exponents.
发表机构
- Higher Education Support Center, Hokkaido University of Science（北海道科学大学高等教育支援中心）
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