On a stratification defined by real roots of polynomials

2002/08/31 by Vladimir Petrov Kostov
Mathematics · #math.AG

paper · pdf

published as Serdica Math. J. 29, No. 2 (2003), 177-186

arxiv created 2002/09/02 · arxiv updated 2009/11/30

Abstract

We consider the family of polynomials P(x,a)=xⁿ+a₁x^n-1+... +a_n, x,a_i∈ \bf R, and the stratification of \bf Rⁿ≅ \(a₁,... ,a_n)|a_i∈ \bf R\ defined by the multiplicity vector of the real roots of P. We prove smoothness of the strata and a transversality property of their tangent spaces.

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