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Ovoidal packings of P G ( 3 , q ) for even q

2013
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Discrete Mathematics
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We show that any set of n pairwise disjoint ovals in a finite projective plane of even order has a unique common tangent. As a consequence, any set of q + 1 pairwise disjoint ovoids in P G(3, q), q even, has exactly q 2 +1 common tangent lines, constituting a regular spread. Also, if q − 1 ovoids in P G(3, q) intersect pairwise exactly in two given points x ̸ = y and share two tangent planes π x , π y at these two points, then these ovoids share exactly (q + 1) 2 common tangent lines, and they

doi:10.1016/j.disc.2013.05.021
fatcat:nl7lqgllpneyxmr4g3wzwzotmu