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Singularités imposables en position générale à une hypersurface projective. (Singularities imposable in general position on a projective surface). (French) Zbl 0675.14025
The question adressed in this paper is the following: Given positive integers n and d, what is the maximal number m such that for a generic configuration of m points in $${\mathbb{P}}^ n$$ there exists a hypersurface of degree $$d$$ in $${\mathbb{P}}^ n$$ having all m points of the configuration as singular points? This question is solved for all n and all $$d\neq 3,4$$. The techniques used are an extension of those in the paper by A. Hirschowitz in Manuscr. Math. 50, 337-338 (1985; Zbl 0571.14002).
Reviewer: H.Knörrer

##### MSC:
 14N10 Enumerative problems (combinatorial problems) in algebraic geometry 14E15 Global theory and resolution of singularities (algebro-geometric aspects) 14J17 Singularities of surfaces or higher-dimensional varieties 14N05 Projective techniques in algebraic geometry
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##### References:
 [1] Hirschowitz, A. : La Méthode d’Horace pour l’interpolation à plusieurs variables . Manuscripta Math. 50 (1985) 337-388. · Zbl 0571.14002 · doi:10.1007/BF01168836 · eudml:155059
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