Parusi\'nski's "Key Lemma" via algebraic geometry
Abstract
The following ``Key Lemma'' plays an important role in Parusinski's work on the existence of Lipschitz stratifications in the class of semianalytic sets: For any positive integer n, there is a finite set of homogeneous symmetric polynomials W1,...,WN in Z[x1,...,xn] and a constant M >0 such that |dxi/xi| M j = 1,..., N |dWj/Wj| as densely defined functions on the tangent bundle of Cn. We give a new algebro-geometric proof of this result.
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