Determinantal Singularities

Research output: Working paper/Preprint › Preprint

Authors

  • Anne Frühbis-Krüger
  • Matthias Pablo Zach

Research Organisations

External Research Organisations

  • Carl von Ossietzky University of Oldenburg
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Details

Original languageEnglish
Publication statusE-pub ahead of print - 9 Jun 2021

Abstract

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.

Cite this

Determinantal Singularities. / Frühbis-Krüger, Anne; Zach, Matthias Pablo.
2021.

Research output: Working paper/Preprint › Preprint

Frühbis-Krüger, A & Zach, MP 2021 'Determinantal Singularities'. <https://arxiv.org/abs/2106.04855>
Frühbis-Krüger, A., & Zach, M. P. (2021). Determinantal Singularities. Advance online publication. https://arxiv.org/abs/2106.04855
Frühbis-Krüger A, Zach MP. Determinantal Singularities. 2021 Jun 9. Epub 2021 Jun 9.
Frühbis-Krüger, Anne ; Zach, Matthias Pablo. / Determinantal Singularities. 2021.
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