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arXiv · 1402.5531

Points de hauteur bornée sur les hypersurfaces de l'espace triprojectif

Teddy Mignot
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Abstract

We establish an asymptotic formula for the number of points of bounded height on a singular hypersurface of the triprojective space. We will see that the final result is in accordance with Batyrev-Manin conjecture. The method used is a version of the circle method developped by Heath Brown and used by Robbiani for counting points of bounded height on an hypersurface of biprojective space. ----- Nous établissons ici une formule asymptotique pour le nombre de points de hauteur bornée sur une hypersurface singulière de l'espace triprojectif. Nous verrons que le résultat obtenu est en accord avec la conjecture de Batyrev-Manin. La méthode utilisée est une version de la méthode du cercle développée par Heath-Brown et reprise par Robbiani pour évaluer le nombre de points rationnels sur une hypersurface de l'espace biprojectif.

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Teddy Mignot. 2014-03-17. Points de hauteur bornée sur les hypersurfaces de l'espace triprojectif. https://arxiv.org/abs/1402.5531

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