Finite image-affine linear spaces Original Research Article

In [The Theory of Finite Linear Spaces. Cambridge University Press, Cambridge, (1993).] Beutelspacher and Kersten studied finite image-semiaffine linear spaces, with image. They characterized those with different point degrees, and in the constant point degree case they obtained a nice characterization of image-semiaffine linear spaces. If image, only the cases image have been studied [W. Hauptmann, Endliche image-Ebenen., Geom. Ded. 9, (1980), 77–86; P. M. Lo Re, D. Olanda, image-semiaffine planes, in: Combinatorics ’88, vol. 2 (Ravello, 1988), Research Lecture Notes Mathematics Mediterranean, Rende, 1991, pp. 195–210.] In this paper we study the case image, image. We determine the point degrees and the line sizes of a image-semiaffine linear space, and we also give some characterization results.