Partial flocks of the quadratic cone yielding Mathon maximal arcs

Abstract

In [6] Hamilton and Thas (2006) describe a link between maximal arcs of Mathon type and partial flocks of the quadratic cone. This link is of a rather algebraic nature. In this paper we establish a geometric connection between these two structures. We also define a composition on the flock planes and use this to work out an analogue of the synthetic version of Mathon’s theorem (see De Clerck et al. (2011) [3]). Finally, we show how it is possible to construct a maximal arc of Mathon type of degree 2d, containing a Denniston arc of degree d provided that there is a solution to a certain given system of trace conditions.