  In this paper we prove under some simplifying hypotheses questions of Picoco
and Levinson-Ullery on Cayley-Bacharach sets. Our results imply that, under
suitable hypotheses Cayley-Bacharach sets lie on curves of low degree. We then
use these results to estimate error terms to the normalized motive of the space
of smooth degree $d$ hypersurfaces in $\mathbb{P}^n$as $d$ grows to infinity.
The error term can be expressed in terms of a certain `sum over points' on
plane cubic curves and the associated Hodge structure can be expressed in terms
of the cohomology of the moduli space of elliptic curves. We also prove
convergence of the motive of degree $d$ hypersurfaces in $\mathbb{P}^n$ as $n$
grows to infinity as well as other results on discriminant complements of high
dimensional varieties.
