Springer and the Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X43520171031Affinization of Segre products of partial linear spaces110111261010ENK.PetelczycInstitute of Mathematics, University of Białystok, Ciołkowskiego 1M, 15-245 Białystok.M.ŻynelInstitute of Mathematics, University of Białystok, Ciołkowskiego 1M, 15-245 Białystok.Journal Article20160405Hyperplanes and hyperplane complements in the Segre product of partial linear spaces are investigated. The parallelism of such a complement is characterized in terms of the point-line incidence. Assumptions, under which the automorphisms of the complement are the restrictions of the automorphisms of the ambient space, are given.<br /> An affine covering for the Segre product of Veblenian gamma spaces is established. A general construction that produces non-degenerate hyperplanes in the Segre product of partial linear spaces embeddable into projective space is introduced.http://bims.iranjournals.ir/article_1010_ae91b745ca8ce73d8145c9d0ba456580.pdf