A Converse to a Theorem on Normal Forms of Volume Forms with Respect to a Hypersurface
[La réciproque d’un théorème sur les formes normales des formes volumes par rapport à une hypersurface]
Kourliouros, Konstantinos1
1 Imperial College London Dept. of mathematics Huxley Building 180 Queen’s Gate London, SW7 (UK)
Annales de l'Institut Fourier, Tome 65 (2015) no. 6, pp. 2437-2447.

Nous donnons ici une réponse positive à une question posée par Y. Colin de Verdière concernant la réciproque du théorème suivant, dû à A. N. Varchenko : deux germes de formes volumes sont équivalents modulo difféomorphismes préservant un germe d’hypersurface à singularités isolées, si leur différence est la différentielle d’une forme dont la restriction sur la partie lisse de l’hypersurface est exacte.

We give here a positive answer to a question asked by Y. Colin de Verdière concerning the converse of the following theorem, due to A. N. Varchenko: two germs of volume forms are equivalent with respect to diffeomorphisms preserving a germ of an isolated hypersurface singularity, if their difference is the differential of a form whose restriction on the smooth part of the hypersurface is exact.

DOI : 10.5802/aif.2992
Classification : 10X99, 14A12, 11L05
Keywords: Isolated Singularities, De Rham Cohomology, Volume Forms, Normal Forms
Mot clés : Singularités Isolées, Cohomologie de de Rham, Formes Volumes, Formes Normales
Kourliouros, Konstantinos 1

1 Imperial College London Dept. of mathematics Huxley Building 180 Queen’s Gate London, SW7 (UK) 
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Kourliouros, Konstantinos. A Converse to a Theorem on Normal Forms of Volume Forms with Respect to a Hypersurface. Annales de l'Institut Fourier, Tome 65 (2015) no. 6, pp. 2437-2447. doi : 10.5802/aif.2992. http://www.numdam.org/articles/10.5802/aif.2992/

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