A remark on some punctual Quot schemes on smooth projective curves

For a locally free sheaf \mathcal{E} on a smooth projective curve, we can define the punctual Quot scheme which parametrizes torsion quotients of \mathcal{E} of length n supported at a fixed point. It is known that the punctual Quot scheme is a normal projective variety with canonical Gorenstein singularities. In this note, we show that the punctual Quot scheme is a \mathbb{Q} -factorial Fano variety of Picard number one.