Translator Disclaimer
Febuary 2020 Tangential approximation of analytic sets
Massimo Ferrarotti, Elisabetta Fortuna, Leslie Wilson
Rocky Mountain J. Math. 50(1): 125-133 (Febuary 2020). DOI: 10.1216/rmj.2020.50.125

Abstract

Two subanalytic subsets of n are called s-equivalent at a common point P if the Hausdorff distance between their intersections with the sphere centered at P of radius r vanishes to order >s as r tends to 0. We strengthen this notion in the case of real subanalytic subsets of n with isolated singular points, introducing the notion of tangential s-equivalence at a common singular point, which considers also the distance between the tangent planes to the sets near the point. We prove that, if V(f) is the zero set of an analytic map f and if we assume that V(f) has an isolated singularity, say at the origin O, then for any s1 the truncation of the Taylor series of f of sufficiently high order defines an algebraic set with isolated singularity at O which is tangentially s-equivalent to V(f).

Citation

Download Citation

Massimo Ferrarotti. Elisabetta Fortuna. Leslie Wilson. "Tangential approximation of analytic sets." Rocky Mountain J. Math. 50 (1) 125 - 133, Febuary 2020. https://doi.org/10.1216/rmj.2020.50.125

Information

Received: 18 July 2019; Accepted: 22 August 2019; Published: Febuary 2020
First available in Project Euclid: 30 April 2020

zbMATH: 07201557
MathSciNet: MR4092547
Digital Object Identifier: 10.1216/rmj.2020.50.125

Subjects:
Primary: 14P15
Secondary: 32B20, 32S05

Rights: Copyright © 2020 Rocky Mountain Mathematics Consortium

JOURNAL ARTICLE
9 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.50 • No. 1 • Febuary 2020
Back to Top