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

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.


14F40 de Rham cohomology and algebraic geometry
33C70 Other hypergeometric functions and integrals in several variables
Full Text: DOI Euclid


[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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