The V 2 2r-1 of PG (2r, q) as a Representation of PG (2, q) : Sections and Partitions

Abstract

This note investigates the hyperplane sections of a ruled variety V 2 2 r − 1 embedded in P G ( 2 r , q ) , which yield caps associated with specific arcs in P G ( 2 , q ) . We construct a partition of the affine points of V 2 2 r − 1 into caps, corresponding to a partition of the affine plane P G ( 2 , q ) into conics.