Finite C3 Geometries in Which All Lines Are Thin.
Finite geometries, varieties and codes.
Finite linear spaces with two more lines than points.
Finite line-transitive linear spaces: Parameters and normal point-partitions.
Finite projective planes, Fermat curves, and Gaussian periods
One of the oldest and most fundamental problems in the theory of finite projective planes is to classify those having a group which acts transitively on the incident point-line pairs (flags). The conjecture is that the only ones are the Desarguesian projective planes (over a finite field). In this paper, we show that non-Desarguesian finite flag-transitive projective planes exist if and only if certain Fermat surfaces have no nontrivial rational points, and formulate several other equivalences involving...
Finite spherical geometries
Flag-transitive extensions of dual affine spaces.