Points de hauteur bornée sur les hypersurfaces lisses des variétés toriques

Volume 172 / 2016

Teddy Mignot Acta Arithmetica 172 (2016), 1-97 MSC: 11D45, 11D72, 11P55. DOI: 10.4064/aa8050-12-2015 Published online: 10 December 2015


We demonstrate the Batyrev–Manin Conjecture for the number of points of bounded height on hypersurfaces of some toric varieties whose rank of the Picard group is 2. The method used is inspired by the one developed by Schindler for the case of hypersurfaces of biprojective spaces and by Blomer and Brüdern for some hypersurfaces of multiprojective spaces. These methods are based on the Hardy–Littlewood circle method. The constant obtained in the final asymptotic formula is the one conjectured by Peyre.


  • Teddy MignotInstitut Fourier, UMR 5582
    UFR de Mathématiques, Université de Grenoble I
    BP 74, 38402 Saint-Martin d’Hères Cedex, France

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