On cubic curves in projective planes of characteristic two

The aim of this paper is to examine various interesting results from the theory of general cub~c curves in projective planes of characteristic two. This leads to calculations involving nets of conics in the plane, invariants of the curves, syzygies, and Hessians. It is emphasized that classical methods, (that is those developed for geometries over fields of zero characteristic), do not always suffice for geometries of differing characteristics. For example, we give here a Hessian of a cubic curve that is a function of degree four in the coefficients of the curve for characteristic two, whereas the classical one has degree three. (The Hessian is used to calculate the points of inflection of a curve.) Particular attention is paid to the case of the planes PG(2, q), where q = 2h, for then the arithmetical and combinatorial properties of the curves come to the fore.