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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

We establish the rationality of simple isolated Cohen–Macaulay codimension 2 (ICMC2) singularities in all dimensions 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.

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singularity, Milnor fiber, vanishing homology, determinantal singularity
Mathematical Subject Classification 2010
Primary: 32S30
Secondary: 14B05
Received: 30 March 2018
Revised: 3 July 2020
Accepted: 22 August 2020
Published: 3 September 2021
Proposed: Walter Neumann
Seconded: Mark Gross, Dan Abramovich
Anne Frühbis-Krüger
Institut fur Mathematik
Carl von Ossietzky Universität Oldenburg
Matthias Zach
Institut für Algebraische Geometrie
Leibniz Universität Hannover