Maximal Arc - Partial Geometries

Partial Geometries

One can construct partial geometries, derived from maximal arcs:

• Let K be a maximal arc with degree d. Consider the incidence structure, where P contains all points of the projective plane not on K, B contains all line of the projective plane intersecting K in d points, and the incidence I is the natural inclusion. This is a partial geometry : .
• Consider the space and let K a maximal arc of degree in a two-dimensional subspace . Consider an incidence structure where P contains all the points not in, B contains all lines not in and intersecting in a point in K, and I is again the natural inclusion. is again a partial geometry : .