2014/03/27 by Teddy Mignot, Mignot, Teddy
Mathematics · #Algebraic Geometry and Number Theory #Holomorphic and Operator Theory #Geometric and Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1403.6975
We prove Batyrev/Manin conjecture for the number of points of bounded height\non some smooth hypersurfaces of the triprojective space of tridegree (1,1,1).\nThe constant appearing in the final result is the one conjectured by Peyre. The\nmethod used is the one developped by Schindler to study the case of\nhypersurfaces of biprojective spaces. This method is based on the\nHardy-Littlewood circle method.\n -----\n Nous d 'emontrons ici la conjecture de Batyrev/Manin pour le nombre de points\nde hauteur born 'ee sur des hypersurfaces de l'espace triprojectif de\ntridegr 'e (1,1,1). La constante obtenue dans le r 'esultat final est celle\nconjectur 'ee par Peyre. La m 'ethode utilis 'ee est celle d 'evelopp 'ee par\nSchindler pour 'etudier le cas des hypersurfaces des espaces biprojectifs.\nCette m 'ethode est essentiellement bas 'ee sur la m 'ethode du cercle de\nHardy-Littlewood.\n