Symplectic translation planes and line ovals

  title={Symplectic translation planes and line ovals},
  author={Antonio Maschietti},
A symplectic spread of a 2n-dimensional vector space V over GFðqÞ is a set of q þ 1 totally isotropic n-subspaces inducing a partition of the points of the underlying projective space. The corresponding translation plane is called symplectic. We prove that a translation plane of even order is symplectic if and only if it admits a completely regular line oval. Also, a geometric characterization of completely regular line ovals, related to certain symmetric designs Sð2d Þ, is given. These results… CONTINUE READING

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