Density of quasismooth hypersurfaces in simplicial toric varieties
Journal de Théorie des Nombres de Bordeaux, Volume 29 (2017) no. 1, pp. 261-288.

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.

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.

Received:
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Accepted:
Published online:
DOI: 10.5802/jtnb.979
Classification: 14J70,  11G25,  14G15,  14M25
Keywords: Bertini theorems, finite fields, toric varieties
Niels Lindner 1

1 Humboldt-Universität zu Berlin Unter den Linden 6 10099 Berlin, Germany
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Niels Lindner. Density of quasismooth hypersurfaces in simplicial toric varieties. Journal de Théorie des Nombres de Bordeaux, Volume 29 (2017) no. 1, pp. 261-288. doi : 10.5802/jtnb.979. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.979/

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