  We consider 18 families of elliptic Calabi--Yaus which arise in constructing
$F$-theory compactifications of string vacua, and show in each case that the
upper Hodge diamond of a crepant resolution of the associated Weierstrass model
coincides with the upper Hodge diamond of the (blown up) projective bundle in
which the crepant resolution is naturally embedded. Such results are
unexpected, as each crepant resolution we consider does \emph{not} satisfy the
hypotheses of the Lefschetz hyperplane theorem. In light of such findings, we
suspect that all ellipitic Calabi--Yaus satisfy such a `Lefschetz-type
phenomenon'.

Algebraic Geometry;High Energy Physics - Theory