The second Veronese ideal I$_{n}$ contains a natural complete
intersection J$_{n}$ of the same height, generated by the principal 2-minors
of a symmetric (n x 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 a direct link in the sense of complete
intersection liaison. 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$_{n}$+ 〈f〉 for an explicit polynomial f constructed
from the fibers of the Veronese grading map.
