Abstract
We study local deformations of singular Lagrangian complete intersections satisfying some nondegeneracy condition. We prove that for a Lagrangian deformation which is infinitesimally Lagrange-versal, the space of relative infinitesimal Lagrangian deformations is a free module over the base of the deformation. In case the deformation is a smoothing, this result implies that the first Betti number of a smoothing is equal to the dimension of the base of a Lagrangian miniversal deformation of the original Lagrangian variety.
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