On Segre's product of partial line spaces and spaces of pencils

In this paper we prove that every collineation of the Segre product of strongly connected partial line spaces is (up to permutation of indices) the product of collineations of its components (Thm. 1.10). Spaces of pencils are strongly connected, so the claim holds for Segre products of them (Thm. 1.14). In the second part we study the extendability of collineations of Segre products of spaces of pencils under some natural embeddings. Received 4 Mai 1998.