Pencils of lines in generalized Laguerre spaces

Abstract

In the paper we characterize subspaces and pencils of lines of generalized (and multidimensional) Laguerre spaces and we consider definability of the structure of "conic" pencils in the Grassmann space of 1-subspaces. We also study definability of the underlying Laguerre geometry in terms of structures of pencils of lines for some, more interesting, systems of pencils.