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The V22r-1 of PG (2r, q) as a Representation of PG (2, q) : Sections and Partitions

DOI: 10.4236/ojdm.2025.154005, PP. 73-85

Keywords: Finite Geometry, Translation Planes, Spreads, Varieties, Caps

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Abstract:

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

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