Geodesic
Parusinski’s “Key Lemma” via algebraic geometry
Reichstein, Z.1 ; Youssin, B.2, 3
1 Department of Mathematics, Oregon State University, Corvallis, OR 97331
2 Department of Mathematics and Computer Science, University of the Negev, Be’er Sheva’, Israel
3 Hashofar 26/3, Ma’ale Adumim, Israel
Electronic research announcements of the American Mathematical Society, Tome 05 (1999), pp. 136-145.

Voir la notice de l'article provenant de la source American Mathematical Society

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 \[ |dx_i/x_i| \le M \max _{j = 1, \dots , N} |dW_j/W_j| \; , \] as densely defined functions on the tangent bundle of $\mathbb {C}^n$. We give a new algebro-geometric proof of this result.
DOI : 10.1090/S1079-6762-99-00072-4

Reichstein, Z. 1 ; Youssin, B. 2, 3

1 Department of Mathematics, Oregon State University, Corvallis, OR 97331
2 Department of Mathematics and Computer Science, University of the Negev, Be’er Sheva’, Israel
3 Hashofar 26/3, Ma’ale Adumim, Israel 
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Reichstein, Z.; Youssin, B. Parusinski’s “Key Lemma” via algebraic geometry. Electronic research announcements of the American Mathematical Society, Tome 05 (1999), pp. 136-145. doi : 10.1090/S1079-6762-99-00072-4. http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-99-00072-4/

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[2] Montgomery, Susan Fixed rings of finite automorphism groups of associative rings 1980

[3] Mumford, D., Fogarty, J., Kirwan, F. Geometric invariant theory 1994

[4] Parusiński, Adam Lipschitz properties of semi-analytic sets Ann. Inst. Fourier (Grenoble) 1988 189 213

[5] Shafarevich, I. R. Basic algebraic geometry 1974

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