Maximal partial spreads in PG (3, q )

Author： Rajola Sandro   Tallini Maria  

Publisher： Springer Publishing Company

ISSN： 0047-2468

Source： Journal of Geometry, Vol.85, Iss.1-2, 2006-09, pp. : 138-148

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Abstract

We transfer the whole geometry of PG(3, q) over a non-singular quadric q4,q of PG(4, q) mapping suitably PG(3, q) over q4,q. More precisely the points of PG(3, q) are the lines of q4,q; the lines of PG(3, q) are the tangent cones of q4,q and the reguli of the hyperbolic quadrics hyperplane section of q4,q. A plane of PG(3, q) is the set of lines of q4,q meeting a fixed line of q4,q. We remark that this representation is valid also for a projective space over any field K and we apply the above representation to construct maximal partial spreads in PG(3, q). For q even we get new cardinalities for For q odd the cardinalities are partially known.

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