Disentanglements of corank 2 map-germs: two examples

TL;DR

This paper computes the homology of multiple point spaces for specific corank 2 map-germs using the image computing spectral sequence, providing detailed examples and an introduction to the method.

Contribution

It offers the first detailed computations of homology for these types of map-germs and introduces the ICSS technique with illustrative examples.

Findings

Homology of multiple point spaces computed for two corank 2 germs.

Application of the image computing spectral sequence (ICSS) to these computations.

The paper includes an accessible introduction to ICSS with low-dimensional examples.

Abstract

We compute the homology of the multiple point spaces of stable perturbations of two germs $(\mathbb{C}^n,0)\to (\mathbb{C}^{n+1},0)$ of corank 2, one with $n=3$ and one with $n=5$. We use a variety of techniques based on the image computing spectral sequence ICSS. We provide a reasonably detailed introduction to the ICSS, including some low-dimensional examples of its use. The paper is partly expository.