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

Abstract : A classical result of Boole shows that, in characteristic 0, the set of singular degree d hypersurfaces in $\mathbb{P}^N$ 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 $\mathbb{P}^N$ of arbitrary codimension and degrees, in any characteristic.
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Submitted on : Thursday, November 7, 2019 - 1:29:38 PM
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Olivier Benoist. Degrés d'homogénéité de l'ensemble des intersections complètes singulières. Annales de l'Institut Fourier, Association des Annales de l'Institut Fourier, 2012, 62 (3), pp.1189-1214. ⟨10.5802/aif.2720⟩. ⟨hal-02353604⟩

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