A-超几何系统的不可约性

The $p$-adic Gelfand-Kapranov-Zelevinsky hypergeometric complex

To a torus action on a complex vector space, Gelfand, Kapranov and Zelevinsky introduce a system of differential equations, which are now called the GKZ hypergeometric system. Its solutions are GKZ hypergeometric functions. We study the $p$-adic counterpart of the GKZ hypergeometric system. The $p$-adic GKZ hypergeometric complex is a twisted relative de Rham complex of over-convergent differential forms with logarithmic poles. It is an over-holonomic object in the derived category of arithmetic $\mathcal D$-modules with Frobenius structures. Traces of Frobenius on fibers at Techmüller points …

Twisted GKZ hypergeometric functions and relative cohomology

We investigate the GKZ $A$-hypergeometric $\mathscr{D}$-modules, introduced by Gel'fand, Kapranov, and Zelevinskii, arising from cyclic covers of toric varieties and find its Riemann--Hilbert partner. This extends our earlier results in arXiv:1902.01536.

关于判别基因座的Horn-Kapranov单值化

On Horn-Kapranov uniformisation of the discriminantal loci

本文给出了非退化仿射完全交簇的判别轨迹的有理一致化方程。为了证明这个公式，我们建立了纤维积分与Horn和Gel'fand-Kapranov-Zelevinski的超几何函数的关系。

Irreducibility of the monodromy representation of Lauricella's $F_C$

Let $E_C$ be the hypergeometric system of differential equations satisfied by Lauricella's hypergeometric series $F_C$ of $m$ variables. We show that the monodromy representation of $E_C$ is irreducible under our assumption consisting of $2^{m+1}$ conditions for parameters. We also show that the monodromy representation is reducible if one of them is not satisfied.

Frobenius structures on hypergeometric equations

We give an exposition of Dwork's construction of Frobenius structures associated to generalized hypergeometric equations via the interpretation of the latter due to Gelfand-Kapranov-Zelevinsky in the language of A-hypergeometric systems. As a consequence, we extract some explicit formulas for the degeneration at 0 in terms of the Morita p-adic gamma function.

$A$ -超几何函数的无穷远点单值性与环面紧化

Monodromy at infinity of $A$-hypergeometric functions and toric compactifications

本文研究了由Gelfand-Kapranov-Zelevinsky引入的$A$ -超几何函数，证明了由平行于坐标轴的复直线上的大环上的解析连续所定义的单值自同构的特征值的一个公式.复曲面紧化的方法将被用来证明我们的主要定理。