The non-existence of ovoids in \(O_ \nu (q)\)
The authors show that the parabolic quadric \(Q (2n,q)\), \(q\) odd, in the projective space \(PG (2n,q)\) does not admit avoids whenever \(n\geq 4\). Their method runs as follows: they associate a certain two-graph to an ovoid and then they show that this two-graph is regular. They calculate the eigenvalues and multiplicities of the corresponding \((0, \pm 1)\)-adjacency matrix. The result follows from expressing that these multiplicities are integers.
scientific article; zbMATH DE number 986979