The Weierstrass semigroups on the quotient curve of a plane curve of degree ≦7 by an involution

First we describe the Weierstrass semigroups on a plane curve of degree ≦6. Using this description we determine the Weierstrass semigroups at a ramification point and a branch point on a double covering from a plane curve of degree ≦6. In the case of a double covering from a plane curve of degree 7 we determine all the Weierstrass semigroups at branch points.