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On
the vanishing topology of isolated Cohen–Macaulay codimension
$2$ singularities
Anne Frühbis-Krüger and Matthias Zach |
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Geometry & Topology 25 (2021) 2167–2194
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Abstract |
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We establish the rationality of simple isolated Cohen–Macaulay codimension (ICMC2) singularities in all dimensions 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
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Mathematical Subject Classification 2010
Primary: 32S30
Secondary: 14B05
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References |
Publication
Received: 30 March 2018
Revised: 3 July 2020
Accepted: 22 August 2020
Published: 3 September 2021
Proposed: Walter Neumann
Seconded: Mark Gross, Dan Abramovich
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Authors |
| Anne Frühbis-Krüger | |
| Institut fur Mathematik Carl von Ossietzky Universität Oldenburg Oldenburg Germany |
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| Matthias Zach | |
| Institut für Algebraische
Geometrie Leibniz Universität Hannover Hannover Germany |
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