Homogeneity degrees of the set of singular complete intersections

Olivier Benoist[1]

  • [1] ENS Paris 45 rue d’Ulm 75005 Paris (France)

Annales de l’institut Fourier (2012)

  • Volume: 62, Issue: 3, page 1189-1214
  • ISSN: 0373-0956

Abstract

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A classical result of Boole shows that, in characteristic 0 , the set of singular degree d hypersurfaces in 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 N of arbitrary codimension and degrees, in any characteristic.

How to cite

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Benoist, Olivier. "Degrés d’homogénéité de l’ensemble des intersections complètes singulières." Annales de l’institut Fourier 62.3 (2012): 1189-1214. <http://eudml.org/doc/251093>.

@article{Benoist2012,
abstract = {Un résultat classique de Boole montre que, sur un corps de caractéristique 0, l’ensemble des hypersurfaces singulières de degré $d$ dans $\mathbb\{P\}^N$ est un diviseur de degré $(N+1)(d-1)^N$ de l’espace projectif de toutes les hypersurfaces. On obtient ici des formules analogues pour des intersections complètes de codimension et de degrés quelconques dans $\mathbb\{P\}^N$, en toute caractéristique.},
affiliation = {ENS Paris 45 rue d’Ulm 75005 Paris (France)},
author = {Benoist, Olivier},
journal = {Annales de l’institut Fourier},
keywords = {Complete intersections; projective duality; toric varieties; finite characteristic},
language = {fre},
number = {3},
pages = {1189-1214},
publisher = {Association des Annales de l’institut Fourier},
title = {Degrés d’homogénéité de l’ensemble des intersections complètes singulières},
url = {http://eudml.org/doc/251093},
volume = {62},
year = {2012},
}

TY - JOUR
AU - Benoist, Olivier
TI - Degrés d’homogénéité de l’ensemble des intersections complètes singulières
JO - Annales de l’institut Fourier
PY - 2012
PB - Association des Annales de l’institut Fourier
VL - 62
IS - 3
SP - 1189
EP - 1214
AB - Un résultat classique de Boole montre que, sur un corps de caractéristique 0, l’ensemble des hypersurfaces singulières de degré $d$ dans $\mathbb{P}^N$ est un diviseur de degré $(N+1)(d-1)^N$ de l’espace projectif de toutes les hypersurfaces. On obtient ici des formules analogues pour des intersections complètes de codimension et de degrés quelconques dans $\mathbb{P}^N$, en toute caractéristique.
LA - fre
KW - Complete intersections; projective duality; toric varieties; finite characteristic
UR - http://eudml.org/doc/251093
ER -

References

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