The asymptotics of points of bounded height on diagonal cubic and quartic threefolds

Authors:
Andreas-Stephan Elsenhans;Jörg Jahnel
Affiliations:
Mathematisches Institut, Universität Göttingen, Göttingen, Germany;Mathematisches Institut, Universität Göttingen, Göttingen, Germany
Venue:
ANTS'06 Proceedings of the 7th international conference on Algorithmic Number Theory
Year:
2006

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Abstract

For the families ax3 = by3 + z3 + v3 + w3, a, b = 1, ... ,100, and ax4 = by4 + z4 + v4 + w4, 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.