An example of the Weierstrass semigroup of a pointed curve on K3 surfaces

Let X be a K3 surface with Picard number one which is given by a double cover π:X→?². Let C be a smooth curve on X with π ^?1 π(C)=C which is not the ramification divisor of π, and let P be a ramification point of π| _C :C→π(C). In this paper, in the case where the intersection multiplicity at π(P) of the curve π(C) and the tangent line at π(P) on π(C) is equal to deg(π(C)) or deg(π(C))?1, we investigate the Weierstrass semigroup of the pointed curve (C,P).