Absolute points of correlations of PG(5,qn)

Abstract

The sets of the absolute points of (possibly degenerate) polarities of a projective space are well known. The sets of the absolute points of (possibly degenerate) correlations, different from polarities, of PG(2,qn) have been completely determined by B.C. Kestenband in 11 papers from 1990 to 2014, for non-degenerate correlations and by J. D'haeseleer and N. Durante in [3] for degenerate correlations. The sets of the absolute points of degenerate correlations, different from degenerate polarities, of PG(3,qn) and PG(4,qn) have been classified respectively in [8] and [10]. In this paper, we consider the five dimensional case and determine the sets of the absolute points of degenerate correlations, different from degenerate polarities, of PG(5,qn). Moreover, we show that some of these sets are related to some ovoids of PG(5,qn).