The Asymptotics of Points of Bounded Height on Diagonal Cubic and Quartic Threefolds

For the families ax4 = by4 +z4 +v4 +w4 , a, b = 1, . . . , 100, and ax3 = by3 + z3 + v3 + w3 , a, b = 1, . . . , 100, of projective algebraic threefolds, we test numerically the conjecture of Manin (in the refined form due to Peyre) about the asymptotics of points of bounded height on Fano varieties.

• Type: Conference
• Year: 2006
• Where: ANTS
• Authors: Andreas-Stephan Elsenhans, Jörg Jahnel
• Keywords: Algorithms, ANTS 2006, Conjecture, Numerically, Projective Algebraic Threefolds