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arXiv · 1611.02625

On discriminants, Tjurina modifications and the geometry of determinantal singularities

Anne Frühbis-Krüger
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Abstract

We describe a method for computing discriminants for a large class of families of isolated determinantal singularities -- more precisely, for subfamilies of ${\mathcal G}$-versal families. 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 on the relation of Milnor and Tjurina numbers for surface singularities.

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Anne Frühbis-Krüger. 2017-05-03. On discriminants, Tjurina modifications and the geometry of determinantal singularities. https://arxiv.org/abs/1611.02625

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