The twisted de Rham complex associated with hypergeometric 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 algebras. 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.
Kazuhiko AOMOTO. Yoshinori MACHIDA. "Double filtration of twisted logarithmic complex and Gauss–Manin connection." J. Math. Soc. Japan 67 (2) 609 - 636, April, 2015. https://doi.org/10.2969/jmsj/06720609