$\mathbb{Z}_n$ acts diagonally. It is a very known fact that the orbifold above admits a crepant resolution (this is an $A_{n-1}$ singularity, so the exceptional set is a chain of $\mathbb{P}^1$'s). Now, if you consider the total space of the canonical bundle of the weighted projective line $\mathbb{P}(1,n-1)$ you have a partial crepant resolution. My question is if this is the unique partial crepant resolution. And of course, I mean that this rsolution is partial because is an intermediate resolution.

I think the question is pretty clear and that is all people here need to know, I guess.

Actually I do not want to consider cases like $\mathbb{P}(2,2)$. I have in mind cases like $\mathbb{P}(1,4)$ and $\mathbb{P}(2,3)$