## Hokkaido Mathematical Journal

### A Lê-Greuel type formula for the image Milnor number

#### 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

https://projecteuclid.org/euclid.hokmj/1550480643

Digital Object Identifier
doi:10.14492/hokmj/1550480643

Mathematical Reviews number (MathSciNet)
MR3914168

Zentralblatt MATH identifier
07055594

#### 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