Topology of Discriminants and Their Complements

  • Victor A. Vassiliev
Conference paper

Abstract

The general notion of a discriminant is as follows. Consider any function space \(\mathcal{F}\), finite dimensional or not, and some class of singularities S that the functions from \(\mathcal{F}\) can take at the points of the issue manifold. The corresponding discriminant variety ∑(S) ⊂ \(\mathcal{F}\) is the space of all functions that have such singular points. For example, let \(\mathcal{F}\) be the space of (real or complex) polynomials of the form
$${x^d} + {a_1}{x^{d - 1}} + \cdots + {a^{d,}}$$
(1)
and S = {a multiple root}.
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Copyright information

© Birkhäser Verlag, Basel, Switzerland 1995

Authors and Affiliations

  • Victor A. Vassiliev
    • 1
    • 2
  1. 1.Independent University of MoscowMoscowRussia
  2. 2.Steklov Mathematical InstituteMoscowRussia

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