Abstract
We study several deformation functors associated to the normalization of a reduced curve singularity \({(X, 0) \subset (\mathbb{C}^n, 0)}\) . The main new results are explicit formulas, in terms of classical invariants of (X, 0), for the cotangent cohomology groups T i, i = 0,1,2, of these functors. Thus we obtain precise statements about smoothness and dimension of the corresponding local moduli spaces. We apply the results to obtain explicit formulas, respectively, estimates for the \({\mathcal{A}_e}\) -codimension of a parametrized curve singularity, where \({\mathcal{A}_e}\) denotes the Mather–Wall group of left-right equivalence.
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Greuel, GM., Le, C.T. On deformations of maps and curve singularities. manuscripta math. 127, 1–21 (2008). https://doi.org/10.1007/s00229-008-0195-6
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DOI: https://doi.org/10.1007/s00229-008-0195-6