Base-point-freeness of double-point divisors of smooth birational-divisors on conical rational scrolls

We work over an algebraically closed field of characteristic zero. The purpose of this paper is to prove that the complete linear system of the double point divisors of smooth birational-divisors on conical rational scrolls are base-point-free. A smooth birational-divisor on a conical rational scroll has a nonbirational inner center, that is a point on it from which the linear projection gives nonbirational map to its image. In the previous paper by the author, it was shown that for a projective variety without nonbirational inner centers, its double point divisor is base-point-free.