Tingting Wen, Shandong University, Chine et UPEC, Evry

Manin's conjecture for singular cubic hypersurfaces

Let S_Q denote the cubic hypersurface x³ = Q(y₁, ..., y_m)z, where Q is a positive definite quadratic form in m variables
with integer coefficients. This S_Q ranges over a class of singular cubic hypersurfaces as Q varies. For S_Q, we prove:

(i) Manin's conjecture is true if Q is locally determined, and we give an explicit asymptotic formula with a power
     saving error term;

(ii) in general Manin's conjecture is true up to a leading constant if m ≥ 6 is even.