  We use topological K-theory to study non-singular varieties with quadratic
entry locus. We thus obtain a new proof of Russo's Divisibility Property for
locally quadratic entry locus manifolds. In particular we obtain a K-theoretic
proof of Zak's theorem that the dimension of a Severi variety must be 2, 4, 8
or 16 and so resolve a conjecture of Atiyah and Berndt. We also show how the
same methods applied to dual varieties recover the Landman parity theorem.
