covering of degree two from a hyperelliptic curve to the projective line are all hyperelliptic Weierstrass points and these exhausts all the Weierstrass points on a hyperelliptic curve of genus . Further information on the gaps comes from applying Clifford's theorem. Multiplication of functions gives the non-gaps a numerical semigroup structure, and an old question of Adolf Hurwitz asked for a characterization of the semigroups occurring. A new necessary condition was found by R.-O. Buchweitz in 1980 and he gave an example of a subsemigroup of the nonnegative integers with 16 gaps that does not occur as the semigroup of non-gaps at a point on a curve of genus 16 (see ). A definition of Weierstrass point for a nonsingular curve over a field of positive characteristic was given by F. K. Schmidt in 1939. Positive characteristic More generally, for a nonsingular algebraic curve defined over an algebraically closed field of characteristic , the gap numbers for all but finitely many points is a fixed sequence These points are called non-Weierstrass points. All points of whose gap sequence is different are called Weierstrass points. If then the curve is called a classical curve. Otherwise, it is called non-classical. In characteristic zero, all curves are classical. Hermitian curves are an example of non-classical curves. These are projective curves defined over finite field by equation , where is a prime power. Notes References Algebraic curves Riemann surfaces