Symplectic Bundles on the Plane, Secant Varieties and Lüroth Quartics Revisited

@inproceedings{Ottaviani2007SymplecticBO,
  title={Symplectic Bundles on the Plane, Secant Varieties and L{\"u}roth Quartics Revisited},
  author={Giorgio Ottaviani},
  year={2007}
}
Let X = P × P embedded with O(1, 2). We prove that its (n + 1)-secant variety σn+1(X) is a hypersurface, while it is expected that it fills the ambient space. The equation of σn+1(X) is the symmetric analog of the Strassen equation. When n = 4 the determinantal map takes σ5(X) to the hypersurface of Lüroth quartics, which is the image of the Barth map… CONTINUE READING