SINGULARITIES OF THE DUAL CURVE OF A CERTAIN PLANE CURVE IN POSITIVE CHARACTERISTIC

It is well known that the Gauss map for a complex plane curve is birational, whereas the Gauss map in positive characteristic is not always birational. Let q be a power of a prime integer. We study a certain plane curve of degree q(2) + q + 1 for which the Gauss map is inseparable with inseparable degree q. As a special case, we show a relation between the dual curve of the Fermat curve of degree q(2) + q + 1 and the Ballico-Hefez curve.