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arXiv · 1009.0704

Degrés d'homogénéité de l'ensemble des intersections complètes singulières

Olivier Benoist
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Abstract

A classical result of Boole shows that, in characteristic 0, the set of singular degree d hypersurfaces in P^N is a divisor of degree (N+1)(d-1)^N in the projective space of all hypersurfaces. We give here analogous formulae for complete intersections in P^N of arbitrary codimension and degrees, in any characteristic. ----- Un resultat classique de Boole montre que, sur un corps de caracteristique 0, l'ensemble des hypersurfaces singulieres de degre d dans P^N est un diviseur de degre (N+1)(d-1)^N de l'espace projectif de toutes les hypersurfaces. On obtient ici des formules analogues pour des intersections completes de codimension et de degres quelconques dans P^N, en toute caracteristique.

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Olivier Benoist. 2012-09-10. Degrés d'homogénéité de l'ensemble des intersections complètes singulières. https://doi.org/10.5802/aif.2720

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