On discriminants, Tjurina modifications and the geometry of determinantal singularities

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

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  • Anne Frühbis-Krüger

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OriginalspracheEnglisch
Seiten (von - bis)375-396
Seitenumfang22
FachzeitschriftTopology and its Applications
Jahrgang234
Frühes Online-Datum24 Nov. 2017
PublikationsstatusVeröffentlicht - 1 Feb. 2018

Abstract

We describe a method for computing discriminants for a large class of families of isolated determinantal singularities – families induced by perturbations of matrices. The approach intrinsically provides a decomposition of the discriminant into two parts and allows the computation of the determinantal and the non-determinantal loci of the family without extra effort; only the latter manifests itself in the Tjurina transform. This knowledge is then applied to the case of Cohen–Macaulay codimension 2 singularities putting several known, but previously unexplained observations into context and explicitly constructing a counterexample to Wahl's conjecture (see [35], section 6) on the relation of Milnor and Tjurina numbers for surface singularities.

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On discriminants, Tjurina modifications and the geometry of determinantal singularities. / Frühbis-Krüger, Anne.
in: Topology and its Applications, Jahrgang 234, 01.02.2018, S. 375-396.

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Frühbis-Krüger A. On discriminants, Tjurina modifications and the geometry of determinantal singularities. Topology and its Applications. 2018 Feb 1;234:375-396. Epub 2017 Nov 24. doi: 10.48550/arXiv.1611.02625, 10.1016/j.topol.2017.11.010
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