The rational homotopy of Thom spaces and the smoothing of isolated singularities
Annales de l'Institut Fourier, Volume 35 (1985) no. 3, pp. 119-135.

Rational homotopy methods are used for studying the problem of the topological smoothing of complex algebraic isolated singularities. It is shown that one may always find a suitable covering which is smoothable. The problem of the topological smoothing (including the complex normal structure) for conical singularities is considered in the sequel. A connection is established between the existence of certain relations between the normal Chern degrees of a smooth projective variety and the question of its realization as a linear section (not necessarily hyperplane).

On utilise les méthodes de l’homotopie rationnelle pour étudier le problème du lissage topologique des singularités algébriques complexes isolées. On montre que, dans toutes les situations, un revêtement convenable peut être lissé. On considère ensuite le problème du lissage topologique (la structure complexe normale y compris) pour les singularités coniques. On établit des liaisons entre l’existence de certaines relations entre les degrés de Chern normaux d’une variété projective lisse et la question de sa réalisation comme section linéaire (pas nécessairement hyperplane).

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     title = {The rational homotopy of {Thom} spaces and the smoothing of isolated singularities},
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Papadima, Stefan. The rational homotopy of Thom spaces and the smoothing of isolated singularities. Annales de l'Institut Fourier, Volume 35 (1985) no. 3, pp. 119-135. doi : 10.5802/aif.1021. http://www.numdam.org/articles/10.5802/aif.1021/

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