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On the Pole Order and Hodge Filtrations of Isolated Hypersurface Singularities

Published online by Cambridge University Press:  20 November 2018

John Scherk*
Affiliation:
Department of Mathematics University of Toronto Toronto, Ontario M5S IAI, e-mail: [email protected]
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Abstract

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Unlike for a smooth projective hypersurface, for an isolated hypersurface singularity, the pole order and Hodge filtrations do not in general coincide. This note studies the difference between the two.

Keywords

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1993

References

[AGV] Arnol'd, V. I., Gusein-Zade, S. M. and Varchenko, A. N., Singularities of differentiable maps, vol. II, Boston-Basel-Stuttgart, Birkhauser, 1985.Google Scholar
[Dimca, D. A., Differential forms and hypersurface singularities, preprint.Google Scholar
[Gr] Griffiths, P., On the periods of certain rational integrals, I, II, Ann. of Math. 90(1960), 460541.Google Scholar
[Grothendieck, G. A., On the DeRham cohomology of algebraic varieties, Publ. Math. I.H.E.S. 29(1966), 95 103.Google Scholar
[K] Karpishpan, Y., Pole order filtration on the cohomology of algebraic links, Compositio Math. 78(1991), 213226.Google Scholar
[P] Pham, F., Singularités des systèmes différentiels de Gauss-Manin, Progress in Mathematics 2, Boston, Birkhauser 1979.Google Scholar
[Sch-St] J. Scherk and Steenbrink, J., On the mixed Hodge structure on the cohomology of the Milnor fibre, Math. Annalen 271(1985), 641665.Google Scholar
[St] Steenbrink, J., Mixed Hodge Structures and Singularities, to appear.Google Scholar