Abstract
Sometimes in a geometry, a residual of a flag F may exhibit objects A and B that appear to belong to classes of distinct types in the residual, but may in fact belong to one type in some covering geometry. The method of realizing such a covering geometry, due to A. Cohen, is exposed. If the covering geometry is connected, A and B belong to one class; if it is not connected, A and B are objects of distinct types. There is some wrestling with sufficient conditions for the latter choice.
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References
Arjeh Cohen. On a theorem of Cooperstein. Euro. J. Combin., 4:107–126, 1983.
Arjeh Cohen. Point-line spaces related to buildings. In F. Buekenhout, editor, Handbook of Incidence Geometry, Chapter 12, pages 647–737. North-Holland, Amsterdam, 1995.
G. Tallini. On a characterization of the Grassmann manifold representing the lines of a projective space. In P. J. Cameron and J. W. P. Hirschfeld, editors, Finite Geometries and Designs: Proceedings of the Second Isle of Thorns Conference, 1980. London Mathematical Society Lecture Notes 49, pages 354–358. Cambridge University Press, Cambridge, 1981.
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Shult, E.E. (2011). Separated Systems of Singular Spaces. In: Points and Lines. Universitext. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15627-4_12
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DOI: https://doi.org/10.1007/978-3-642-15627-4_12
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