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April, 2015 Double filtration of twisted logarithmic complex and Gauss–Manin connection
Kazuhiko AOMOTO, Yoshinori MACHIDA
J. Math. Soc. Japan 67(2): 609-636 (April, 2015). DOI: 10.2969/jmsj/06720609


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.


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Kazuhiko AOMOTO. Yoshinori MACHIDA. "Double filtration of twisted logarithmic complex and Gauss–Manin connection." J. Math. Soc. Japan 67 (2) 609 - 636, April, 2015.


Published: April, 2015
First available in Project Euclid: 21 April 2015

zbMATH: 1336.14018
MathSciNet: MR3340189
Digital Object Identifier: 10.2969/jmsj/06720609

Primary: 33C70
Secondary: 14F40

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

Rights: Copyright © 2015 Mathematical Society of Japan


Vol.67 • No. 2 • April, 2015
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