  The second Veronese ideal $I_n$ contains a natural complete intersection
$J_n$ generated by the principal $2$-minors of a symmetric $(n\times
n)$-matrix. We determine subintersections of the primary decomposition of $J_n$
where one intersectand is omitted. If $I_n$ is omitted, the result is the other
end of a complete intersection link as in liaison theory. These
subintersections also yield interesting insights into binomial ideals and
multigraded algebra. For example, if $n$ is even, $I_n$ is a Gorenstein ideal
and the intersection of the remaining primary components of $J_n$ equals
$J_n+\langle f \rangle$ for an explicit polynomial $f$ constructed from the
fibers of the Veronese grading map.
