Parusiński's "Key Lemma" via algebraic geometry

1999/10/26 by Zinovy Reichstein, Boris Youssin
Mathematics · #math.AG

paper · pdf

published as Electronic Research Announcements of AMS 5 (1999), 136-145. · 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

arxiv created 1999/10/26 · arxiv updated 2009/11/30

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,...,W_N in Z[x₁,...,x_n] and a constant M >0 such that |dx_i/x_i| ≤ M max_{j = 1,..., N} |dW_j/W_j| as densely defined functions on the tangent bundle of Cⁿ. We give a new algebro-geometric proof of this result.

Related

• The Gauss--skizze decomposition is a Goresky-MacPherson stratification
• A Maximal Extension of the Best-Known Bounds for the Furstenberg-Sárközy Theorem
• Demailly's conjecture on Waldschmidt constants for sufficiently many very general points in ℙⁿ
• Homogeneous Forms Inequalities
• Polynomials as Lipschitz maps on the Veronese cone