A rigidity theorem for Lagrangian deformations

Details A rigidity theorem for Lagrangian deformations A rigidity theorem for Lagrangian deformations

2003-05-28

arxiv.org/abs/math/0305394v3

Mathematics

Algebraic Geometry

17 pages

Scientific paper

We consider deformations of singular Lagrangian varieties in symplectic spaces. We show the coherence of the direct image sheaves of relative infinitesimal Lagrangian deformations. Using this result, we prove that, under some assumptions, a Lagrangian deformation is analytically rigid provided that this is the case infinitesimally. This gives generalisations of recent results by Colin de Verdi\`ere concerning Lagrangian curves.

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