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Aomoto, Kazuhiko; Machida, Yoshinori

Double filtration of twisted logarithmic complex and Gauss-Manin connection. (English) Zbl 1336.14018

J. Math. Soc. Japan 67, No. 2, 609-636 (2015).
The authors study the twisted de Rham complex associated to a finite family of complex polynomials of the same degree and satisfying some genericity conditions. This complex is compared to complexes of logarithmic differential forms, which are endowed with a natural double filtration. This approach gives new information on the bases for the twisted de Rham cohomology.
Reviewer: Alexandru Dimca (Nice)

Cited in 2 Documents

MSC:

14F40 de Rham cohomology and algebraic geometry
33C70 Other hypergeometric functions and integrals in several variables

Keywords:

hypergeometric integrals; twisted de Rham complex; logarithmic forms; filtrations
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\textit{K. Aomoto} and \textit{Y. Machida}, J. Math. Soc. Japan 67, No. 2, 609--636 (2015; Zbl 1336.14018)
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References:

[1] K. Aomoto, Les équations aux différences linéaires et les intégrales des fonctions multiformes, J. Fac. Sci. Univ. Tokyo Sect. IA Math., 22 (1975), 271-297. · Zbl 0339.35021
[2] K. Aomoto, Une correction et un complément à l’article “Les équations aux différences linéaires et les intégrales des fonctions multiformes”, J. Fac. Sci. Univ. Tokyo Sect. IA Math., 26 (1979), 519-523. · Zbl 0425.35022
[3] K. Aomoto and M. Kita, Theory of Hypergeometric Functions, Springer Monogr. Math., Springer-Verlag, 2011. · Zbl 1229.33001
[4] K. Aomoto, M. Kita, P. Orlik and H. Terao, Twisted de Rham cohomology groups of logarithmic forms, Adv. Math., 128 (1997), 119-152. · Zbl 0905.14010
[5] D. Eisenbud, The Geometry of Syzygies, Grad. Texts in Math., 229 , Springer-Verlag, 2005. · Zbl 1066.14001
[6] W. Gröbner, Moderne Algebraische Geometrie, Springer-Verlag, 1949. · Zbl 0033.12706
[7] M. Kita and M. Noumi, On the structure of cohomology groups attached to the integral of certain many-valued analytic functions, Japan J. Math. (N.S.), 9 (1983), 113-157. · Zbl 0549.32003
[8] K. Saito, On a generalization of de-Rham lemma, Ann. Inst. Fourier (Grenoble), 26 (1976), 165-170. · Zbl 0338.13009
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