K-theory, LQEL manifolds and Severi varieties

Abstract

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.

17 pages; added references; minor corrections

References in corpus (2)

• Varieties with quadratic entry locus, I
• Manifolds covered by lines and the Hartshorne Conjecture for quadratic manifolds