Result: The Samuel stratification of the discriminant is Whitney regular
Title:
The Samuel stratification of the discriminant is Whitney regular
Authors:
Source:
Geometriae Dedicata. 17
Publisher Information:
Springer Science and Business Media LLC, 1984.
Publication Year:
1984
Subject Terms:
polynomials having a multiple root, discriminant, Representations of entire functions of one complex variable by series and integrals, Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral), versal deformation, Stratifications in topological manifolds, Stratifications, constructible sheaves, intersection cohomology (complex-analytic aspects), Samuel stratification, canonical Whitney stratification, 0101 mathematics, 01 natural sciences, space of unitary polynomials, Stratified sets
Document Type:
Academic journal
Article
File Description:
application/xml
Language:
English
ISSN:
1572-9168
0046-5755
0046-5755
DOI:
10.1007/bf00151505
Access URL:
Rights:
Springer TDM
Accession Number:
edsair.doi.dedup.....e421d093cce6f9dc9f4fb9f33f8f37af
Database:
OpenAIRE
Further Information
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 \(A_{n-1}\).