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Article Dans Une Revue Mathematische Zeitschrift Année : 2022

Quantitative Curve Selection Lemma

Saugata Basu
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Résumé

We prove a quantitative version of the curve selection lemma. Denoting by $s,d,k$ a bound on the number, the degree and the number of variables of the polynomials describing a semi-algebraic set $S$ and a point $x$ in $\bar S$, we find a semi-algebraic path starting at $x$ and entering in $S$ with a description of degree $(O(d)^{3k+3},O(d)^{k})$ (using a precise definition of the description of a semi-algebraic path and its degree given in the paper). As a consequence, we prove that there exists a semi-algebraic path starting at $x$ and entering in $S$, such that the degree of the Zariski closure of the image of this path is bounded by $O(d)^{4k+3}$, improving a result of Jelonek and Kurdyka.

Dates et versions

hal-01763372 , version 1 (11-04-2018)

Identifiants

Citer

Saugata Basu, Marie-Françoise Roy. Quantitative Curve Selection Lemma. Mathematische Zeitschrift, 2022, 300 (3), pp.2349-2361. ⟨10.1007/s00209-021-02837-0⟩. ⟨hal-01763372⟩
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