Dimca, Alexander; Rosian, Rodica The Samuel stratification of the discriminant is Whitney regular. (English) Zbl 0557.57010 Geom. Dedicata 17, 181-184 (1984). Let A denote the space of unitary polynomials \(x^ n+a_ 1x^{n- 1}+...+a_ n\), \(a_ i\in {\mathbb{C}}\) of degree n. The discriminant \(D\subset A\) is the algebraic hypersurface consisting of those polynomials having a multiple root. The Samuel stratification of the discriminant is the partition of D into the subsets \(D^ m=\{a\in D\); \(mult_ a(D)=m\}\) of constant multiplicity. It is shown that this Samuel stratification coincides with the canonical Whitney stratification of the algebraic set D. The proof is based on the connection between the discriminant D and the versal deformation of the fat point \(X_ 0:x^ n=0\) of type \(A_{n-1}\). Cited in 1 Review MSC: 57N80 Stratifications in topological manifolds 32S60 Stratifications; constructible sheaves; intersection cohomology (complex-analytic aspects) 30C15 Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) 58A35 Stratified sets 30D10 Representations of entire functions of one complex variable by series and integrals Keywords:space of unitary polynomials; discriminant; polynomials having a multiple root; Samuel stratification; canonical Whitney stratification; versal deformation PDFBibTeX XMLCite \textit{A. Dimca} and \textit{R. Rosian}, Geom. Dedicata 17, 181--184 (1984; Zbl 0557.57010) Full Text: DOI