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A rigidity theorem for Lagrangian deformations

Published online by Cambridge University Press:  04 December 2007

Mauricio D. Garay
Mauricio D. Garay
Affiliation:
Fachbereich Mathematik 17, Staudingerweg 9, Johannes Gutenberg-Universität, 55099 Mainz, Germanygaray@mathematik.uni-mainz.de
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Abstract

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We consider deformations of singular Lagrangian varieties in symplectic manifolds. We prove that a Lagrangian deformation of a Lagrangian complete intersection is analytically rigid provided that this is the case infinitesimally. This result is given as a consequence of the coherence of the direct image sheaves of relative infinitesimal Lagrangian deformations.

Keywords

normal form theorysymplectic geometryintegrable systemsLagrangian varieties70H0632S65
Type
Research Article
Information
Compositio Mathematica , Volume 141 , Issue 6 , November 2005 , pp. 1602 - 1614
Copyright
Foundation Compositio Mathematica 2005