Non-isomorphic semipartial geometries
In DeWinter and Thas (Des Codes Cryptogr, 32, 1530-166, 2004) a semipartial geometry S((U) over bar) was constructed from any Buekenhout-Metz unital U in PG(2, q(2)), and it was shown that, although having the same parameters, S((U) over bar) not congruent to T-2(*)(U), where T-2(*)(U) is the semipartial geometry arising from the linear representation of U. In this note, we will first briefly overview what is known on the geometry S((U) over bar) (providing shortened unpublished proofs for most results). Then we answer the following question of G. Ebert affirmatively: "Do non-isomorphic Buekenhout0-Metz unitals U-1 and U-2 yield non-isomorphic semipartial geometries S((U) over bar (1)) and S((U) over bar (2))?".
semipartial geometry (buekenhout-metz) unital