Moduli of sheaves on ribbons

Abstract

We study the geometry of the moduli stack of torsion-free sheaves on ribbons. We introduce a stratification of the stack by the complete type of the sheaves, and we investigate the geometric properties of the strata and their closure relation, and which strata intersect the (semi)stable locus. Then we describe the irreducible components of the stack, by revealing an interesting trichotomy between Fano, Calabi-Yau and canonically polarized cases. Finally, we compute the tangent space of the moduli stack at a given sheaf.