Keywords
- Differential Form
- Spectral Sequence
- Curve Singularity
- Hodge Structure
- Hodge Number
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References
Arnold, V.I.: Normal forms of Poisson structures and of other powers of volume forms, Tr. Sem. I.G. Petrovskogo, 12, 1–15 (1985).
Arnold, V.I., Gusein-Zade, S.M., Varchenko, A.N.: Singularities of Differentiable Maps, vol. I, Monographs in Math. 82, Birkhäuser 1985.
Briançon, J., Skoda, H.: Sur la cloture intégrale d'un idéale de germes de fonctions holomorphes en un point de ℂn, C.R. Acad. Sci. Paris 278, 949–951 (1974).
Brieskorn, E.: Die Monodromie der isolierten Singularitäten von Hyperflächen, Manuscripta math. 2, 103–161 (1970).
Brieskorn, E., Knörrer, H.: Plane Algebraic Curves, Birkhäuser 1986.
Deligne, P.: Theorie de Hodge II, III, Publ. Math. IHES 40, 5–58 (1971) and 44, 5–77 (1974).
Deligne, P., Dimca, A.: Filtrations de Hodge et par l'ordre du pôle pour les hypersurfaces singulières Ann. Sci. Ec. Norm. Sup. (to appear).
Dimca, A.: On analytic abelian coverings, Math. Ann. 279, 501–515 (1988).
Dimca, A.: On the Milnor fibrations of weighted homogeneous polynomials, Compositio Math. (to appear).
Dimca, A.: Betti numbers of hypersurfaces and defects of linear systems, Duke Math. J. 60, 285–298 (1990).
Dimca, A.: On the de Rham cohomology of a hypersurface complement, Amer. J. Math. (to appear).
Durfee, A.H.: Mixed Hodge structures on punctured neighborhoods, Duke Math. J. 50, 1017–1040 (1983).
Greuel, G.-M.: Der Gauss-Manin-Zusammenhang isolierter Singularitäten von vollständigen Durchschnitten, Math. Ann. 214, 235–266 (1975).
Grothendieck, A.: On the de Rham cohomology of algebraic varieties, Publ. Math. IHES 29, 351–358 (1966).
Karpishpan, Y.: Pole order filtration on the cohomology of algebraic links (preprint MIT).
Kouchnirenko, A.G.: Polyèdres de Newton et nombres de Milnor, Invent. Math. 32, 1–31 (1976).
Looijenga, E.J.N.: Isolated Singular Points on Complete Intersections, London Math. Soc. Lecture Note Series 77, Cambridge Univ. Press, 1984.
Malgrange, B.: Intégrales asymptotiques et monodromie, Ann. Sci. Ecole Norm. Sup. 7, 405–430 (1974).
Milnor, J.: Singular Points of Complex Hypersurfaces. Ann. of Math. Studies 61, Princeton Univ. Press, 1968.
Orlik. P., Solomon, P., Solomon, L.: Singularities I, Hypersurfaces with an isolated singularity, Adv. in Math. 27, 256–272 (1978).
Saito, K.: Quasihomogene isolierte Singularitäten von Hyperflächen, Invent. Math. 14, 123–142 (1971).
Scheja, G., Wiebe, H.: Über Derivationen in isolierten Singularitäten auf vollständigen Durchschnitten, Math. Ann. 225, 161–171 (1977).
Scherk, J.: Isolated Singular Points and the Gauss-Manin Connection, D. Ph. Thesis, Oxford, 1977.
Scherk, J.: On the monodromy theorem for isolated hypersurface singularities, Invent. Math. 58, 289–301 (1980).
Scherk, J., Steenbrink, J.H.M.: On the mixed Hodge structure on the cohomology of the Milnor fiber, Math. Ann. 271, 641–665 (1985).
Steenbrink, J.H.M.: Intersection form for quasihomogeneous singularities, Compositio Math. 34, 211–223 (1977).
Steenbrink, J.H.M.: Mixed Hodge structure on the vanishing cohomology. In: Holm, P. ed.: Real and Complex Singularities, pp. 525–563, Oslo 1976, Alphen aan de Rijn Sijthoff, Noordhoff 1977.
Steenbrink, J.H.M.: Mixed Hodge structures associated with isolated singularities, Proc. Symp. Pure Math. 40, Part 2, pp. 513–536 (1983).
Steenbrink, J.H.M.: Mixed Hodge Structures and Singularities (book to appear).
Varchenko, A.N.: Asymptotic Hodge structure in the vanishing cohomology, Math. USSR Izv. 18, 469–512 (1982).
Varchenko, A.N.: Local classification of volume forms in the presence of a hypersurface, Funct. Anal. Appl. 19 (4), 269–276 (1985).
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© 1991 Springer-Verlag Berlin Heidelberg
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Dimca, A. (1991). Differential forms and hypersurface singularities. In: Mond, D., Montaldi, J. (eds) Singularity Theory and its Applications. Lecture Notes in Mathematics, vol 1462. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0086378
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DOI: https://doi.org/10.1007/BFb0086378
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