On discriminants, Tjurina modifications and the geometry of determinantal singularities

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Authors

  • Anne Frühbis-Krüger

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Details

Original languageEnglish
Pages (from-to)375-396
Number of pages22
JournalTopology and its Applications
Volume234
Early online date24 Nov 2017
Publication statusPublished - 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.

Keywords

    Discriminants for families of determinantal singularities, EIDS, Geometry of determinantal singularities, Invariants of determinantal singularities, Tjurina modification

Cite this

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

Research output: Contribution to journal › Article › Research › 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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