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Parusinski’s “Key Lemma” via algebraic geometry. (English) Zbl 0956.32009
Summary: The following “key lemma” plays an important role in the work by Parusiński 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 $$W_1, \dots ,W_N$$ in $$Z[x_1,\dots,x_n]$$ and a constant $$M>0$$ such that $|dx_i/x_i|\leq M \max_{j = 1, \dots, N} |dW_j/W_j|,$ as densely defined functions on the tangent bundle of $${\mathbb C}^n$$. We give a new algebro-geometric proof of this result.

##### MSC:
 32B20 Semi-analytic sets, subanalytic sets, and generalizations 14P15 Real-analytic and semi-analytic sets
##### Keywords:
semianalytic sets; tangent bundle
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##### References:
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