  A ribbon is a first-order thickening of a non-singular curve. Motivated by a
question of Eisenbud and Green, we show that a compactification of the moduli
space of line bundles on a ribbon is given by the moduli space of semi-stable
sheaves. We then describe the geometry of this space, determining the
irreducible components, the connected components, and the smooth locus.

Algebraic Geometry