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Vanishing topology of codimension 1 multi-germs over $\Bbb R$ and $\Bbb C$

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Cooper, T., Mond, D. (David) and Wik Atique, R.. (2002) Vanishing topology of codimension 1 multi-germs over $\Bbb R$ and $\Bbb C$. Compositio Mathematica, Vol.13 (No.2). pp. 121-160. ISSN 0010-437X

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Official URL: http://dx.doi.org/10.1023/A:1014930205374

Abstract

We construct all $\cal A$e-codimension 1 multi-germs of analytic (or smooth) maps (kn, T) [rightward arrow] (kp, 0), with n [gt-or-equal, slanted] p − 1, (n, p) nice dimensions, k = $\mathbb C$ or $\mathbb R$, by augmentation and concatenation operations, starting from mono-germs (|T| = 1) and one 0-dimensional bi-germ. As an application, we prove general statements for multi-germs of corank [less-than-or-eq, slant] 1: every one has a real form with real perturbation carrying the vanishing homology of the complexification, every one is quasihomogeneous, and when n = p − 1 every one has image Milnor number equal to 1 (this last is already known when n [gt-or-equal, slanted] p).

Item Type:

Journal Article

Subjects:

Q Science > QA Mathematics

Divisions:

Faculty of Science > Mathematics

Library of Congress Subject Headings (LCSH):

Perturbation (Mathematics), Topology, Discriminant analysis, Singularities (Mathematics), Deformations of singularities

Journal or Publication Title:

Compositio Mathematica

Publisher:

Cambridge University Press

ISSN:

0010-437X

Official Date:

April 2002

Dates:

Date	Event
April 2002	Published

Volume:

Vol.13

Number:

No.2

Page Range:

pp. 121-160

Identification Number:

10.1023/A:1014930205374

Status:

Peer Reviewed

Access rights to Published version:

Open Access

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