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Let R be a local ring Noetherian, e.g. power series in several variables. Denote by Mat(m,n,R)
the space of matrices with entries in R.
Various groups act on this space.
We study the corresponding Tjurina modules, the tangent spaces to the miniversal deformation.
The first step is to check whether/ when these modules are finite dimensional. (This ensures the
finite determinacy.) We compute/bound the support of these modules, achieving numerous geometric
criteria of determinacy.
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