Gluing two affine spaces
The author presents a detailed study of the gluing of two affine spaces over a commutative field \(K\) following the general theory described by \textit{F. Buekenhout}, \textit{C. Huybrechts} and the author in Bull. Belg. Math. Soc. Simon Stevin 1, No. 3, 355-397 (1994; Zbl 0809.51012) where some of these results were first announced. The author proves that the canonical gluing of two copies of \(AG (n,K)\) is a quotient of a certain subgeometry of the building of type \(D_{n + 1}\) over \(K\). The author also shows that the canonical gluing of two copies of the point-line system of \(AG (n,q)\) is characterized by its automorphism groups, which is as large as possible. Furthermore, with the exception of two cases, this gluing is characterized by a flag-transitivity condition.
scientific article; zbMATH DE number 885627