On cluster categories of weighted projective lines with at most three weights

Let X be a weighted projective line and CX the associated cluster category. It is known that can realized as generalized category of quiver with potential. In this note, under assumption has at most three weights or tubular type, we prove if C(Q,W) Jacobi-finite non-degenerate potential (Q,W) shares 2-CY tilted algebra CX, then triangle equivalent to CX. As byproduct, determined by its provided weights. end, for any weights, also obtain realization via Buan-Iyama-Reiten-Scott's construction categories arising from preprojective algebras.