# K–theory, LQEL manifolds and Severi varieties

@article{Nash2014KtheoryLM, title={K–theory, LQEL manifolds and Severi varieties}, author={O. Nash}, journal={Geometry & Topology}, year={2014}, volume={18}, pages={1245-1260} }

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. 14M22; 19L64

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