TITLE:
The V22r-1 of PG (2r, q) as a Representation of PG (2, q) : Sections and Partitions
AUTHORS:
Rita Vincenti
KEYWORDS:
Finite Geometry, Translation Planes, Spreads, Varieties, Caps
JOURNAL NAME:
Open Journal of Discrete Mathematics,
Vol.15 No.4,
August
27,
2025
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.