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 ]
Annales de l'Institut Fourier, Tome 65 (2015) no. 6, p. 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 : https://doi.org/10.5802/aif.2992
Classification:  10X99,  14A12,  11L05
Mots clés: Singularités Isolées, Cohomologie de de Rham, Formes Volumes, Formes Normales
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     author = {Kourliouros, Konstantinos},
     title = {A Converse to a Theorem on Normal Forms of Volume Forms with Respect to a Hypersurface},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {65},
     number = {6},
     year = {2015},
     pages = {2437-2447},
     doi = {10.5802/aif.2992},
     zbl = {1336.32029},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2015__65_6_2437_0}
}
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/item/AIF_2015__65_6_2437_0/

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