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}
}
  • O. Nash
  • Published 2014
  • Mathematics
  • Geometry & Topology
  • 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 

    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 30 REFERENCES
    Varieties with quadratic entry locus, I
    42
    On dual defective manifolds
    7
    Varieties with small dual varieties, I
    127
    Tangents and Secants of Algebraic Varieties
    426
    On degenerate secant and tangential varieties and local differential geometry
    39
    The Projective Geometry of Freudenthal's Magic Square
    108
    Manifolds covered by lines and the Hartshorne Conjecture for quadratic manifolds
    18
    Varieties of small codimension in projective space
    139
    Projective Duality and Homogeneous Spaces
    59
    Projective planes, Severi varieties and spheres
    31