| Abstract |
Abstract: Affine algebraic geometry is the study of zero sets V (I) ⊆ K^n where I is an ideal I⊆ K[x_1,...,x_n]. A point on a variety V(I) is called singular if the tangent space at that point has not expected dimension. In this talk, I am interested to talk about the affine algebraic variety in a neighbourhood of a point (for instant singular points) and parametrization of space curve singularities. We consider instead of the global object V (I) the germs (V (I), p), p ∈ V (I). In the case of irreducible curves, we have a normalization map K[[x_1, ..., x_n]]/ < I>→ K[[t]] inducing a parametrization of the curve. In the case of plane curve singularities the parameterization is given by Puiseux Expansion.
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