Singular bielliptic curves and special linear systems

Here we study the Brill–Noether theory of special linear systems on a singular Gorenstein bielliptic curve Y. Any such linear system is associated to a spanned rank 1 torsion-free sheaf, L. We obtain the same results as in the case of a smooth curve if either Lset membership, variantPic(Y) or Y has only ordinary nodes or ordinary cusps as singularities.