Sectional Singularities and Geometry of Families of Planar Quadratic Forms

  • J. W. Bruce
  • V. V. Goryunov
  • V. M. Zakalyukin
Part of the Trends in Mathematics book series (TM)


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 [2] and [3]. 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.


Symmetric Matrice Betti Number Dynkin Diagram Short Cycle Sectional Singularity 
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Copyright information

© Springer Basel AG 2002

Authors and Affiliations

  • J. W. Bruce
    • 1
  • V. V. Goryunov
    • 1
  • V. M. Zakalyukin
    • 2
  1. 1.Department of Mathematical SciencesUniversity of LiverpoolLiverpoolUK
  2. 2.Department of Mechanics and MathematicsMoscow Lomonosov State UniversityMoscowRussia

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