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Literature Cited
V. I. Arnol'd, "Normal forms of functions near degenerate critical points, the Weyl groups Ak, Dk, Ek, and Lagrangian singularities," Funkts. Anal. Prilozhen.,5, No. 4, 3–25 (1972).
V. I. Arnol'd, "Critical points of functions on manifolds with boundary, simple Lie groups Bk, Ck, F4, and singularities of evolutes," Usp. Mat. Fiz.,33, No. 5, 91–105 (1978).
V. I. Arnol'd, A. N. Varchenko, and S. M. Gusein-Zade, Singularities of Differentiable Maps [in Russian], Vol. 1, Nauka, Moscow (1982).
V. I. Arnol'd, A. N. Varchenko, and S. M. Gusein-Zade, Singularities of Differentiable Maps [in Russian], Vol. 2, Nauka, Moscow (1984).
I. N. Bernshtein, "Analytic continuation of generalized functions with respect to a parameter," Funkts. Anal. Prilozhen.,6, No. 4, 26–40 (1972).
A. N. Varchenko, "Semicontinuity of the spectrum and an upper bound for the number of singular points of a projective hypersurface," Dokl. Akad. Nauk SSSR,270, No. 6, 1294–1297 (1983).
A. N. Varchenko, "Local classification of volume forms in the presence of a hypersurface," Funkts. Anal. Prilozhen.,19, No. 4, 23–31 (1985).
A. N. Varchenko, "Combinatorics and topology of the disposition of affine hyperplanes in real space," Funkts. Anal. Prilozhen.,21, No. 1, 11–22 (1987).
V. A. Vasil'ev, I. M. Gel'fand, and A. V. Zelevinskii, "General hypergeometric functions on complex Grassmanians," Funkts. Anal. Prilozhen.,21, No. 1, 23–38 (1987).
A. B. Givental’, "Lagrangian manifolds with singularities and irreducible sℓ2-modules," Usp. Mat. Nauk,38, No. 6, 109–110 (1983).
A. B. Givental’ and V. V. Shekhtman, "Monodromy groups and Hecke algebras," Usp. Mat. Nauk,42, No. 4, 138 (1987).
V. V. Goryunov, "Geometry of bifurcation diagrams of simple projections to a line," Funkts. Anal. Prilozhen.,15, No. 2, 1–8 (1981).
P. Griffiths and J. Harris, Principles of Algebraic Geometry [Russian translation], Mir, Moscow (1982).
V. P. Kostov, "Versal deformations of differential forms of degree α on the line," Funkts. Anal. Prilozhen.,18, No. 4, 81–82 (1984).
S. K. Lando, "Normal forms of powers of the volume form," Funkts. Anal. Prilozhen.,19, No. 2, 78–79 (1985).
J. Milnor, Singular Points of Complex Hypersurfaces [Russian translation], Mir, Moscow (1971).
F. Fam, "Generalized Picard—Lefschetz formulas and branched integrals," Matematika,13, No. 4, 61–93 (1969).
K. Aomoto, "On the structure of integrals of power product of linear functions," Sc. Papers Coll. General Educ. Univ. Tokyo,27, 49–61 (1977).
T. Kohno, "Linear representations of braid groups and classical Yang—Baxter equation," in: Artin's Braid Groups, Santa Cruz (1987).
J. Steenbrink, "Mixed Hodge structure on the vanishing cohomology," in: Real and Complex Singularities, Nordic Summer School, Oslo (1976).
J. Steenbrink, "Semicontinuity of the singularity spectrum," Invent. Math.,79, No. 3, 557–565 (1985).
W. Ebeling, "On the monodromy groups of singularities," in: Proc. Symp. Pure Math., Vol. 40, Part 1 (1983), pp. 327–336.
S. V. Chmutov, "Monodromy groups of singularities of functions of two variables," Funkts. Anal. Prilozhen.,15, No. 1, 61–66 (1981).
G. G. Il'yuta, "Monodromy and vanishing cycles of boundary singularities," Funkts. Anal. Prilozhen.,19, No. 3, 11–21 (1985).
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Institute of Chemical Physics, Academy of Sciences of the USSR. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 22, No. 1, pp. 12–22, January–March, 1988.
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Givental’, A.B. Twisted Picard-Lefschetz formulas. Funct Anal Its Appl 22, 10–18 (1988). https://doi.org/10.1007/BF01077718
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DOI: https://doi.org/10.1007/BF01077718