K–theory, LQEL manifolds and Severi varieties

Nash, Oliver¹

¹ Dublin, Ireland

Geometry & topology, Tome 18 (2014) no. 3, pp. 1245-1260.

Résumé

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.

Détail

DOI : 10.2140/gt.2014.18.1245

Classification : 14M22, 19L64
Keywords: $K$–theory, secant variety, Severi variety, quadric, dual variety

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