Determinantal Singularities

Anne Frühbis-Krüger () and Matthias Zach ()
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Anne Frühbis-Krüger: Carl-von-Ossietzky Universität Oldenburg
Matthias Zach: Leibniz Universität Hannover

Chapter Chapter 2 in Handbook of Geometry and Topology of Singularities IV, 2023, pp 45-159 from Springer

Abstract: 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 ( ℂ 3 , 0 ) $$({\mathbb C}^3,0)$$ 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.

Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-31925-9_2

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DOI: 10.1007/978-3-031-31925-9_2

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