Monads for framed sheaves on Hirzebruch surfaces

TL;DR

This paper introduces monads for framed torsion-free sheaves on Hirzebruch surfaces, enabling the construction of smooth moduli spaces that are fine and possess universal monads.

Contribution

It defines monads for framed sheaves on Hirzebruch surfaces and constructs smooth, fine moduli spaces with universal monads.

Findings

Moduli spaces are smooth algebraic varieties.

Moduli spaces are fine with universal monads.

Framework applies to framed torsion-free sheaves on Hirzebruch surfaces.

Abstract

We define monads for framed torsion-free sheaves on Hirzebruch surfaces and use them to construct moduli spaces for these objects. These moduli spaces are smooth algebraic varieties, and we show that they are fine by constructing a universal monad.