Let X be a 2-dimensional affine toric variety over an algebraically closed field k of characteritic 0. We consider a way to construct from X the Weierstrass semigroup H of a point on a complete non-singular curve over k such that the minimal embedding of its monomial curve Spec kH into the affine space is derived from that of X by substituting monomials. For any n≧2 we give examples of such X and H where H is generated by n elements.
Jiryo Komeda (Thu,) studied this question.