Double filtration of twisted logarithmic complex and Gauss–Manin connection

Double filtration of twisted logarithmic complex and Gauss–Manin connection
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扭曲对数复数和高斯-马宁连接的双重过滤

DOI：
10.2969/jmsj/06720609
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
Y. Machida
Y. Machida
中科院分区：
--
文献类型：
--
作者：
K. Aomoto;Y. Machida

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.与多项式幂积的超几何积分相关的扭曲de Rham复形与相应的对数复形是拟同构的。我们在这篇文章中表明，后者有一个关于多项式和外代数次数的双重过滤。利用组合方法证明了同阶多项式的扭de Rham上同调与特殊滤波子复形之间的拟同构.这一事实给出了一个更详细的结构的基础扭曲德拉姆上同调。
. The twisted de Rham complex associated with hypergeo- metric integral of a power product of polynomials is quasi-isomorphic to the corresponding logarithmic complex. We show in this article that the latter has a double filtration with respect to degrees of polynomials and exterior al-gebras. By a combinatorial method we prove the quasi-isomorphism between the twisted de Rham cohomology and a specially filtered subcomplex in case of polynomials of the same degree. This fact gives a more detailed structure of a basis for the twisted de Rham cohomology.