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Comptes Rendus Mathématique
Volume 335, n° 1
pages 5-10 (2002)
Doi : S1631-073X(02)02423-8
Received : 14 February 2002 ;  accepted : 29 April 2002
Structures de Poisson sur une intersection complète à singularités isolées
Poisson structures over a complete intersection with isolated singularities
 

Benoit Fresse
Laboratoire J.A. Dieudonné, Université de Nice, Parc Valrose, 06108 Nice cedex 02, France 

Note présentée par Jean-Louis Koszul

Résumé

On étudie les structures de Poisson sur des variétés singulières. On considère dans ce but le complexe de Koszul associé aux équations d'une intersection complète. Ce complexe forme une algèbre différentielle graduée qui est équivalente à l'algèbre de la variété. On montre qu'une structure de Poisson est équivalente à la donnée d'une famille de multidérivations sur le complexe de Koszul. Si notre variété a des singularités isolées, alors on peut construire une telle famille de multidérivations de forme réduite. Pour citer cet article : B. Fresse, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 5-10.

The full text of this article is available in PDF format.
Abstract

We study Poisson structures over singular varieties. For this purpose, we consider the Koszul complex associated to the equations of a complete intersection. This complex forms a differential graded algebra which is equivalent to the algebra of the variety. We show that a Poisson structure is equivalent to a sequence of multiderivations over the Koszul complex. If the variety has isolated singularities, then we can construct a sequence of multiderivations of reduced form. To cite this article: B. Fresse, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 5-10.

The full text of this article is available in PDF format.


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