Algebraic Geometry/Analytic Geometry
Unobstructed Lagrangian deformations
Comptes Rendus. Mathématique, Volume 338 (2004) no. 8, pp. 617-622.

We prove that deformations of a Lagrangian singularity are unobstructed if the usual (flat) deformations are unobstructed and if a cohomological vanishing condition is satisfied. This gives another application to deformation theory of the Lagrangian de Rham complex introduced in Sevenheck and van Straten (Math. Ann. 327 (1) (2003) 79–102). To prove our theorem, we use the T1-lifting criterion due to Ran, Kawamata and others.

On démontre que les déformations d'une singularité lagrangienne ne sont pas obstruées si le foncteur des déformations plates est lisse et si une condition d'annulation cohomologique est satisfaite. Ceci donne une autre application à la théorie des déformations du complexe de de Rham lagrangien introduit dans Sevenheck et van Straten (Math. Ann. 327 (1) (2003) 79–102). Le théorème est prouvé grâce à un critère de relèvement de déformations infinitésimales dû à Ran, Kawamata et d'autres.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2004.02.006
Sevenheck, Christian 1

1 École normale supérieure, département de mathématiques et applications, 45, rue d'Ulm, 75230 Paris cedex 05, France
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Sevenheck, Christian. Unobstructed Lagrangian deformations. Comptes Rendus. Mathématique, Volume 338 (2004) no. 8, pp. 617-622. doi : 10.1016/j.crma.2004.02.006. http://www.numdam.org/articles/10.1016/j.crma.2004.02.006/

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