Abstract
Given a partition of a projective 3-space of odd cardinality by a set of ovoids, a line secant to one of the ovoids of the partition, and its polar relative to the symplectic polarity on the projective 3-space defined by this ovoid, are tangent to distinct ovoids of the partition (Theorem 2). The proof uses the fact that the radical of the linear code generated by the duals of the hyperbolic quadrics in a symplectic generalized quadrangle is of codimension one (Theorem 4).
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Communicating Editor: Manoj K Yadav
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Sastry, N.S.N., Shukla, R.P. Ovoidal fibrations in \({\pmb {PG}}\varvec{(3,q)}, {\pmb {q}}\) even. Proc Math Sci 130, 65 (2020). https://doi.org/10.1007/s12044-020-00594-4
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DOI: https://doi.org/10.1007/s12044-020-00594-4