Hokkaido Mathematical Journal

A Lê-Greuel type formula for the image Milnor number

J. J. NUÑO-BALLESTEROS and I. PALLARÉS-TORRES

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

Let $f:(\mathbb{C}^n,0)\rightarrow (\mathbb{C}^{n+1},0)$ be a corank 1 finitely determined map germ. For a generic linear form $p:(\mathbb{C}^{n+1},0)\to(\mathbb{C},0)$ we denote by $g:(\mathbb{C}^{n-1},0)\rightarrow (\mathbb{C}^{n},0)$ the transverse slice of $f$ with respect to $p$. We prove that the sum of the image Milnor numbers $\mu_I(f)+\mu_I(g)$ is equal to the number of critical points of $p|_{X_s}:X_s\to\mathbb{C}$ on all the strata of $X_s$, where $X_s$ is the disentanglement of $f$ (i.e., the image of a stabilisation $f_s$ of $f$).

Article information

Source
Hokkaido Math. J., Volume 48, Number 1 (2019), 45-59.

Dates
First available in Project Euclid: 18 February 2019

Permanent link to this document
https://projecteuclid.org/euclid.hokmj/1550480643

Digital Object Identifier
doi:10.14492/hokmj/1550480643

Mathematical Reviews number (MathSciNet)
MR3914168

Zentralblatt MATH identifier
07055594

Subjects
Primary: 32S30: Deformations of singularities; vanishing cycles [See also 14B07]
Secondary: 32S05: Local singularities [See also 14J17] 58K40: Classification; finite determinacy of map germs

Keywords
Image Milnor number Lê-Greuel formula finite determinacy

Citation

NUÑO-BALLESTEROS, J. J.; PALLARÉS-TORRES, I. A Lê-Greuel type formula for the image Milnor number. Hokkaido Math. J. 48 (2019), no. 1, 45--59. doi:10.14492/hokmj/1550480643. https://projecteuclid.org/euclid.hokmj/1550480643


Export citation