Journal of the Mathematical Society of Japan

Double filtration of twisted logarithmic complex and Gauss–Manin connection

Kazuhiko AOMOTO and Yoshinori MACHIDA

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Abstract

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.

Article information

Source
J. Math. Soc. Japan, Volume 67, Number 2 (2015), 609-636.

Dates
First available in Project Euclid: 21 April 2015

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1429624597

Digital Object Identifier
doi:10.2969/jmsj/06720609

Mathematical Reviews number (MathSciNet)
MR3340189

Zentralblatt MATH identifier
1336.14018

Subjects
Primary: 33C70: Other hypergeometric functions and integrals in several variables
Secondary: 14F40: de Rham cohomology [See also 14C30, 32C35, 32L10]

Keywords
hypergeometric integrals twisted de Rham cohomology logarithmic forms de Rham–Saito Lemma vanishing theorem double filtration Gauss–Manin connection

Citation

AOMOTO, Kazuhiko; MACHIDA, Yoshinori. Double filtration of twisted logarithmic complex and Gauss–Manin connection. J. Math. Soc. Japan 67 (2015), no. 2, 609--636. doi:10.2969/jmsj/06720609. https://projecteuclid.org/euclid.jmsj/1429624597


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References

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