Аннотация:We use topological K-theory to study nonsingular 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 answer a question of Atiyah and Berndt.We also show how the same methods applied to dual varieties recover the Landman parity theorem.
