A Duality Result for Moduli Spaces of Semistable Sheaves Supported on Projective Curves

We show that the map sending a sheaf to its dual gives an isomorphism of the moduli space of semistable sheaves with fixed multiplicity and Euler characteristic and supported on projective curves to the moduli space of semistable sheaves of dimension one on the projective space with the same multiplicity but with opposite Euler characteristic.