Parusi\'nski's "Key Lemma" via algebraic geometry
Algebraic Geometry
2007-05-23 v3
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 W_1,...,W_N in Z[x_1,...,x_n] and a constant M >0 such that |dx_i/x_i| \le M \max_{j = 1,..., N} |dW_j/W_j| as densely defined functions on the tangent bundle of C^n. We give a new algebro-geometric proof of this result.
Cite
@article{arxiv.math/9910064,
title = {Parusi\'nski's "Key Lemma" via algebraic geometry},
author = {Zinovy Reichstein and Boris Youssin},
journal= {arXiv preprint arXiv:math/9910064},
year = {2007}
}
Comments
Only abstract has been changed in this revision. AMS LaTeX 1.1, 10 pages. Author-supplied dvi file available at http://ucs.orst.edu/~reichstz/pub.html