GKZ Hypergeometric Structures
GKZ Hypergeometric Structures
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GKZ 超几何结构
DOI：
10.1007/978-3-7643-8284-1_12
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发表时间：
2005
影响因子：
2.3
通讯作者：
J. Stienstra
中科院分区：
文献类型：
--
作者：
J. Stienstra
本文基于作者2005年6月在伊斯坦布尔举办的暑期学校代数几何和超几何函数的讲座。本文回顾了Gelfand、Kapranov和Zelevinsky的超几何结构理论的一些基本方面，包括微分方程、积分和级数，重点介绍了后者。次级扇被构建并随后用于描述Γ-series收敛域的“地理”。给出了若干共振问题的解法，并将其应用于镜像对称。整篇文章给出了许多例子和一些练习。
This text is based on lectures by the author in the Summer School Algebraic Geometry and Hypergeometric Functions in Istanbul in June 2005. It gives a review of some of the basic aspects of the theory of hypergeometric structures of Gelfand, Kapranov and Zelevinsky, including Differential Equations, Integrals and Series, with emphasis on the latter. The Secondary Fan is constructed and subsequently used to describe the ‘geography’ of the domains of convergence of the Γ-series. A solution to certain Resonance Problems is presented and applied in the context of Mirror Symmetry. Many examples and some exercises are given throughout the paper.