Using the local parametrization theorem, prove that if (X,p) is an irreducible germ of a subvariety of dimension greater than 1, then there exists a neighborhood U of p and a closed subvar...Using the local parametrization theorem, prove that if (X,p) is an irreducible germ of a subvariety of dimension greater than 1, then there exists a neighborhood U of p and a closed subvariety X⊂U (whose germ at p is (X,p)), such that for every q∈X there exists an irreducible subvariety Y⊂X of dimension 1 such that p∈Y and q∈Y.
