Gabor Nagy:
Projective embeddings of k-nets
We investigate k-nets embedded in the projective plane defined over a field;
they are line configurations consisting of k pairwise disjoint line-sets,
called components, such that any two lines from distinct families are
concurrent with exactly one line from each component. The size of each
component of a k-net is the same, the order of the k-net. If the field has
zero characteristic, no embedded k-net for k>=5 exists. Here we prove that
this holds true in positive characteristic p as long as p is sufficiently
large compared with the order of the k-net. Our approach, also provides a
new proof in characteristic zero.