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Dual grid; elliptic quadric; Frobenius reciprocity; Tits ovoid.

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).

N S NARASIMHA SASTRY¹ R P SHUKLA²

1. Indian Institute of Technology, Walmi Campus, Belur Industrial Area, Near High Court, P.B. Road, Dharawad 580 011, India
2. Department of Mathematics, University of Allahabad, Prayagraj 211 002, India

Published

13 November 2020

Final version published online

13 November 2020