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On a stratification defined by real roots of polynomials

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Vladimir Petrov Kostov

Algebraic Geometry · Submitted 28 Aug 2002

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We prove smoothness of the strata and a transversality property of their tangent spaces.

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arXiv IDmath/0208219 (version 2)
Pith IDB7P7DFFM, Pith's permanent record of this paper and its review
CitationVladimir Petrov Kostov. "On a stratification defined by real roots of polynomials." arXiv:math/0208219 (2002). https://pith.science/paper/B7P7DFFM
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,419 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.05 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.03 · mentions code or data availability 0.01.

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arXiv listing abstract v2. Results and the main claim are underlined; .

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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#sentencerolethe authors' own workstates the main conclusionstrength
s0 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 $P$. contribution 0.55 0.63 0.05 asserted 0.77
s1 We prove smoothness of the strata and a transversality property of their tangent spaces. result 0.88 0.96 0.86 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original 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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