Sectional Singularities and Geometry of Families of Planar Quadratic Forms
We show that, for hypersurface sections (in the sense of Damon) of isolated functions singularities, the Tjurina and Milnor numbers coincide. An application of this to the families of 2 × 2 symmetric and arbitrary matrices proves the conjectures naturally arising from the results of  and . In addition, we study the vanishing homology of the determinantal curves of two-parameter families of symmetric order 2 matrices and construct Dynkin diagrams of simple singularities of such families.
KeywordsSymmetric Matrice Betti Number Dynkin Diagram Short Cycle Sectional Singularity
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