On the representation of configurations in projective spaces
The author discusses embeddings of point-line configurations into projective spaces over a field. A heuristic condition is found that depends upon an invariant called freedom. The author discusses algorithmic methods that implement embeddings. This is applied to \(k_3\)-configurations, which consist of \(k\) points and \(k\) lines, with 3 points on every line and 3 lines through every point. It is shown that every connected \(k_3\)-configuration can be reduced to a single equation, which can be solved to describe every planar embedding. All higher dimensional embeddings can be obtained by lifting these planar embeddings.
scientific article; zbMATH DE number 1471126