6533b853fe1ef96bd12aca73
RESEARCH PRODUCT
A characterization of the line set of an odd-dimensional Baer subspace
Johannes Ueberbergsubject
Set (abstract data type)CombinatoricsDiscrete mathematicsCardinalityBlocking setLine (geometry)Geometry and TopologyCharacterization (mathematics)Type (model theory)Linear subspaceSubspace topologyMathematicsdescription
Generalizing a theorem of Beutelspacher and Seeger, we consider line sets\(\mathcal{L}\) inP=PG(2t + 1,q),t ∈ IN, with the following properties: (1) any (t + 1)-dimensional subspace ofP contains at least one line of\(\mathcal{L}\), (2) if a pointx ofP is incident with at least two lines of\(\mathcal{L}\) then the points in the factor geometryP/x which are induced by the lines of\(\mathcal{L}\) throughx form a blocking set of type (t, 1) inP/x, (3) any line of\(\mathcal{L}\) is coplanar with at least one further line of\(\mathcal{L}\). We will show that the examples of minimal cardinality are exactly the line sets of Baer subspaces ofP.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1990-04-01 | Journal of Geometry |