A-hypergeometric sustems that come from geometry
A-hypergeometric sustems that come from geometry
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A-来自几何的超几何系统
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
S. Sperber
中科院分区：
文献类型：
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作者：
A. Adolphson;S. Sperber
在最近的工作中，Beukers 描述了具有全套代数解的 A 超几何系统。他通过 (1) 确定哪些 A-超几何系统具有几乎所有素数 p 的全套以 p 为模的解，以及 (2) 表明这些系统来自几何学，从而实现了这一目标。然后，他应用了 N. Katz 的基本定理，该定理表明此类系统具有全套代数解。在本文中，我们在非共振 A 超几何系统和 de Rhamtype 复合体之间建立了一些联系，从而确定了哪些 A 超几何系统来自几何。我们不利用系统不可约这一事实，也不寻找其解决方案的积分公式。
In recent work, Beukers characterized A-hypergeometric systems having a full set of algebraic solutions. He accomplished this by (1) determining which A-hypergeometric systems have a full set of solutions modulo p for almost all primes p and (2) showing that these systems come from geometry. He then applied a fundamental theorem of N. Katz, which says that such systems have a full set of algebraic solutions. In this paper we establish some connections between nonresonant A-hypergeometric systems and de Rhamtype complexes, which leads to a determination of which A-hypergeometric systems come from geometry. We do not use the fact that the system is irreducible or find integral formulas for its solutions.