Stable pairs on curves and surfaces

TL;DR

This paper develops stability conditions for pairs of sheaves and homomorphisms on projective varieties, constructing their moduli spaces on curves and surfaces, with applications to Higgs pairs and framed bundles.

Contribution

It introduces new stability conditions for pairs and constructs their moduli spaces on curves and surfaces, including notable examples like Higgs pairs and framed bundles.

Findings

Established stability conditions for pairs on curves and surfaces.

Constructed moduli spaces for these pairs.

Provided examples including Higgs pairs and framed bundles.

Abstract

We describe stability conditions for pairs consisting of a coherent sheaf and a homomorphism to a fixed coherent sheaf on a projective variety. The corresponding moduli spaces are constructed for pairs on curves and surfaces. We consider two examples. The fixed sheaf is the structure sheaf or is a vector bundle on a divisor, i.e. Higgs pairs or framed bundles, resp. (unencoded version)