Cet article a pour objet la densité des hypersurfaces dans une variété torique projective, normale et simpliciale sur un corps fini ayant une intersection quasi-lisse avec un sous-schéma quasi-lisse fixé. Le résultat géneralise la formule trouvée par B. Poonen pour des variétés projectives lisses. Comme application, nous analysons en outre la densité des hypersurfaces dont le nombre des singularités et la longueur du schéma singulier sont bornés.
This paper investigates the density of hypersurfaces in a projective normal simplicial toric variety over a finite field having a quasismooth intersection with a given quasismooth subscheme. The result generalizes the formula found by B. Poonen for smooth projective varieties. As an application, we further analyze the density of hypersurfaces with bounds on their number of singularities and on the length of their singular schemes.
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Mots clés : Bertini theorems, finite fields, toric varieties
@article{JTNB_2017__29_1_261_0,
author = {Lindner, Niels},
title = {Density of quasismooth hypersurfaces in simplicial toric varieties},
journal = {Journal de th\'eorie des nombres de Bordeaux},
pages = {261--288},
publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
volume = {29},
number = {1},
year = {2017},
doi = {10.5802/jtnb.979},
language = {en},
url = {http://www.numdam.org/articles/10.5802/jtnb.979/}
}
TY - JOUR AU - Lindner, Niels TI - Density of quasismooth hypersurfaces in simplicial toric varieties JO - Journal de théorie des nombres de Bordeaux PY - 2017 SP - 261 EP - 288 VL - 29 IS - 1 PB - Société Arithmétique de Bordeaux UR - http://www.numdam.org/articles/10.5802/jtnb.979/ DO - 10.5802/jtnb.979 LA - en ID - JTNB_2017__29_1_261_0 ER -
%0 Journal Article %A Lindner, Niels %T Density of quasismooth hypersurfaces in simplicial toric varieties %J Journal de théorie des nombres de Bordeaux %D 2017 %P 261-288 %V 29 %N 1 %I Société Arithmétique de Bordeaux %U http://www.numdam.org/articles/10.5802/jtnb.979/ %R 10.5802/jtnb.979 %G en %F JTNB_2017__29_1_261_0
Lindner, Niels. Density of quasismooth hypersurfaces in simplicial toric varieties. Journal de théorie des nombres de Bordeaux, Tome 29 (2017) no. 1, pp. 261-288. doi : 10.5802/jtnb.979. http://www.numdam.org/articles/10.5802/jtnb.979/
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