Characterization of Hermitian varieties by cutting gaps

Determine whether the list of cutting gaps given in Theorem 4.3 characterizes non-degenerate Hermitian varieties among quasi-Hermitian varieties.

Background

The paper introduces the k-th cutting gap to measure whether the intersection of a point set with every k-dimensional subspace spans that subspace. For a non-degenerate Hermitian variety, Theorem 4.3 gives an explicit list of cutting gaps according to the codimension of the subspaces. The authors leave unresolved whether this pattern is sufficient to distinguish Hermitian varieties from the broader class of quasi-Hermitian varieties, which share the same hyperplane intersection numbers as Hermitian varieties.