Abstract
We study modular subspaces corresponding to two deformation functors associated with an isolated singularity X 0: the functor \(Def_{X_0 }\) of deformations of X 0 and the functor \(Def_{X_0 }^s\) 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 \(Def_{X_0 }^s\) of quasi-homogeneous complete intersection singularities coincide. Then flatness conditions for the first cotangent cohomology modules of the deformation functors under consideration are compared.
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Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 15, Theory of Functions, 2004.
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Hirsch, T., Martin, B. Deformations with Section: Cotangent Cohomology, Flatness Conditions, and Modular Subgerms. J Math Sci 132, 739–756 (2006). https://doi.org/10.1007/s10958-006-0020-2
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DOI: https://doi.org/10.1007/s10958-006-0020-2