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 Cet article a éte moissonné depuis la source American Mathematical Society

Voir la notice de l'article

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 
@article{10_1090_S1079_6762_99_00072_4,
     author = {Reichstein, Z. and Youssin, B.},
     title = {Parusinski{\textquoteright}s {{\textquotedblleft}Key} {Lemma{\textquotedblright}} via algebraic geometry},
     journal = {Electronic research announcements of the American Mathematical Society},
     pages = {136--145},
     year = {1999},
     volume = {05},
     doi = {10.1090/S1079-6762-99-00072-4},
     url = {http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-99-00072-4/}
}
TY  - JOUR
AU  - Reichstein, Z.
AU  - Youssin, B.
TI  - Parusinski’s “Key Lemma” via algebraic geometry
JO  - Electronic research announcements of the American Mathematical Society
PY  - 1999
SP  - 136
EP  - 145
VL  - 05
UR  - http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-99-00072-4/
DO  - 10.1090/S1079-6762-99-00072-4
ID  - 10_1090_S1079_6762_99_00072_4
ER  - 
%0 Journal Article
%A Reichstein, Z.
%A Youssin, B.
%T Parusinski’s “Key Lemma” via algebraic geometry
%J Electronic research announcements of the American Mathematical Society
%D 1999
%P 136-145
%V 05
%U http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-99-00072-4/
%R 10.1090/S1079-6762-99-00072-4
%F 10_1090_S1079_6762_99_00072_4
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

[1] Bourbaki, N. Éléments de mathématique. 23. Première partie: Les structures fondamentales de l’analyse. Livre II: Algèbre. Chapitre 8: Modules et anneaux semi-simples 1958

[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

Cité par Sources :