$A$-超几何级数内蕴扰动的余维数公式
A codimension formula for intrinsic perturbation of $A$-hypergeometric series
- Graduate School of Science, Hokkaido University（北海道大学大学院理学研究院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文研究齐次$A$-超几何系统在一般方向上的典范形式解空间，给出内蕴扰动得到的典范级数张成子空间的余维数公式，并证明该余维数至少为$\lceil 3q^2/4\rceil$。
AI中文摘要：
我们研究齐次$A$-超几何系统在一般方向上的典范形式解空间。我们将该空间除以由内蕴扰动得到的典范级数（取遍该空间中出现的所有指数以及所有有序负支撑族）张成的子空间，将其表示为一个有限维余核，并计算该子空间的余维数。我们证明该表示及余维数可传递到共同非奇异域上的全纯解。我们将这些结果应用于格秩为2、具有$5q$列（对每个整数$q\geq 1$）的齐次$A$-超几何系统，并证明由内蕴扰动得到的典范级数张成的子空间在典范形式解空间中的余维数至少为$\lceil 3q^2/4\rceil$。
英文摘要：
We study the canonical formal solution space of a homogeneous $A$-hypergeometric system in a generic direction. We present as a finite-dimensional cokernel the quotient of that space by the span of the canonical series obtained by intrinsic perturbation, taken over all exponents occurring in that space and all ordered negative support families, and we compute the codimension of that span. We show that the presentation and the codimension transfer to the holomorphic solutions on a common nonsingular domain. We apply these results, for every integer $q\geq 1$, to a homogeneous $A$-hypergeometric system of lattice rank 2 with $5q$ columns and show that the span of the canonical series obtained by intrinsic perturbation has codimension at least $\lceil 3q^2/4\rceil$ in the canonical formal solution space.
