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On a stratification defined by real roots of polynomials

Vladimir Petrov Kostov
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Abstract

We consider the family of polynomials $P(x,a)=x^n+a_1x^{n-1}+... +a_n$, $x,a_i\in {\bf R}$, and the stratification of ${\bf R}^n\cong \{(a_1,... ,a_n)|a_i\in {\bf R}\}$ 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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Vladimir Petrov Kostov. 2002-09-02. On a stratification defined by real roots of polynomials. https://arxiv.org/abs/math/0208219

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