Moduli of sheaves on ribbons

TL;DR

This paper explores the geometric structure of the moduli stack of torsion-free sheaves on ribbons, including stratification, irreducible components, and tangent space computations, revealing rich geometric classifications.

Contribution

It introduces a stratification based on sheaf types, analyzes the stack's irreducible components, and computes tangent spaces, advancing understanding of sheaf moduli on ribbons.

Findings

Identification of stratification by sheaf type

Description of irreducible components with Fano, Calabi-Yau, cases

Explicit tangent space computations at sheaves

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.