#### Volume 25, issue 5 (2021)

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On the vanishing topology of isolated Cohen–Macaulay codimension $2$ singularities

### Anne Frühbis-Krüger and Matthias Zach

Geometry & Topology 25 (2021) 2167–2194
##### Abstract

We establish the rationality of simple isolated Cohen–Macaulay codimension $2$ (ICMC2) singularities in all dimensions $\ge 2$ and explicitly compute the vanishing homology of a certain class of threefolds including all the simple ones. ICMC2 singularities are determinantal and can be viewed as a natural generalization of complete intersections. The main tool for our investigations is the so-called Tjurina transformation — a special blowup construction based on the determinantal structure and often compatible with deformations.

##### Keywords
singularity, Milnor fiber, vanishing homology, determinantal singularity
Primary: 32S30
Secondary: 14B05