  We study modular subspaces corresponding to two deformation functors
associated to an isolated singularity X_0: the functor Def_{X_0} of
deformations of X_0 and the functor Def^s_{X_0} of deformations with section of
X_0. 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 Def_{X_0} and Def^s_{X_0} of quasihomogeneous complete
intersection singularities coincide. Flatness conditions for the first
cotangent cohomology modules of the deformation functors under consideration
are then compared.
