Determinantal Singularities
| Autor: | Frühbis-Krüger, Anne, Zach, Matthias |
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| Rok vydání: | 2021 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We survey determinantal singularities, their deformations, and their topology. This class of singularities generalizes the well studied case of complete intersections in several different aspects, but exhibits a plethora of new phenomena such as for instance non-isolated singularities which are finitely determined, or smoothings with low connectivity; already the union of the coordinate axes in $(\mathbb{C}^3,0)$ is determinantal, but not a complete intersection. We start with the algebraic background and then continue by discussing the subtle interplay of unfoldings and deformations in this setting, including a survey of the case of determinantal hypersurfaces, Cohen-Macaulay codimension $2$ and Gorenstein codimension $3$ singularities, and determinantal rational surface singularities. We conclude with a discussion of essential smoothings and provide an appendix listing known classifications of simple determinantal singularities. Comment: 68 pages, 11 figures |
| Databáze: | arXiv |
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