Deformations with section: Cotangent cohomology, flatness conditions and modular subgerms
Tobias Hirsch, Bernd Martin
Abstract
We study modular subspaces corresponding to two deformation functors associated to an isolated singularity X0: the functor DefX0 of deformations of X0 and the functor DefsX0 of deformations with section of X0. After recalling some standard facts on the cotangent cohomology of analytic algebras and the general theory of deformations with section, we give several criteria for modularity in terms of the relative cotangent cohomology modules of a deformation. In particular it is shown that the modular strata for the functors DefX0 and DefsX0 of quasihomogeneous complete intersection singularities coincide. Flatness conditions for the first cotangent cohomology modules of the deformation functors under consideration are then compared.
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