On a conjecture of Wooley and lower bounds for cubic hypersurfaces

V. Vinay Kumaraswamy, Nick Rome

Let $X\subset {\mathbf{P}}_{\mathbf{Q}}^{n-1}$ be a cubic hypersurface cut out by the vanishing of a non-degenerate rational cubic form in $n$ variables. Let $N(X,B)$ denote the num…