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Electronic Research Announcements

ISSN 1079-6762



Parusinski’s “Key Lemma” via algebraic geometry

Authors: Z. Reichstein and B. Youssin
Journal: Electron. Res. Announc. Amer. Math. Soc. 5 (1999), 136-145
MSC (1991): Primary 14E15, 14F10, 14L30; Secondary 16S35, 32B10, 58A40
Published electronically: November 17, 1999
MathSciNet review: 1728678
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Abstract | References | Similar Articles | Additional Information

Abstract: 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.

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Additional Information

Z. Reichstein
Affiliation: Department of Mathematics, Oregon State University, Corvallis, OR 97331
MR Author ID: 268803

B. Youssin
Affiliation: Department of Mathematics and Computer Science, University of the Negev, Be’er Sheva’, Israel
Address at time of publication: Hashofar 26/3, Ma’ale Adumim, Israel

Received by editor(s): October 16, 1999
Published electronically: November 17, 1999
Additional Notes: Z. Reichstein was partially supported by NSF grant DMS-9801675 and (during his stay at MSRI) by NSF grant DMS-9701755.
Communicated by: David Kazhdan
Article copyright: © Copyright 1999 American Mathematical Society