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

让 $\mathbb{X}$ 成为加权投影线，并且 ${\mathcal{C}}_{\mathbb{X}}$相关的群集类别。众所周知${\mathcal{C}}_{\mathbb{X}}$可以实现为具有潜力的颤动的广义簇类别。在本说明中，假设$\mathbb{X}$ 最多具有三个权重或属于管状类型，我们证明如果广义聚类类别 ${\mathcal{C}}_{（问，\mathrm{w\; ^}）}$ 势的Jacobi有限非退化颤抖 $（问，\mathrm{w\; ^}）$ 与之共享2CY倾斜代数 ${\mathcal{C}}_{\mathbb{X}}$， 然后 ${\mathcal{C}}_{（问，\mathrm{w\; ^}）}$ 三角形等于 ${\mathcal{C}}_{\mathbb{X}}$。作为副产物，2-CY倾斜代数为${\mathcal{C}}_{\mathbb{X}}$ 由它的颤动决定，前提是 $\mathbb{X}$最多具有三个权重。最后，对于任何加权投影线$\mathbb{X}$ 最多包含三个权重，我们还获得了 ${\mathcal{C}}_{\mathbb{X}}$ 通过Buan-Iyama-Reiten-Scott构造了由前投影代数引起的2-CY类。