Moduli spaces of framed flags of sheaves on the projective plane

TL;DR

This paper explores the structure of moduli spaces of framed flags of sheaves on the projective plane, demonstrating their irreducibility, smoothness, and symplectic properties for specific invariants.

Contribution

It introduces an adapted ADHM construction for these moduli spaces and proves their geometric properties under certain conditions.

Findings

Moduli space is irreducible and nonsingular.

The space carries a holomorphic pre-symplectic form.

Results depend on specific topological invariants.

Abstract

We study the moduli space of framed flags of sheaves on the projective plane via an adaptation of the ADHM construction of framed sheaves. In particular, we prove that, for certain values of the topological invariants, the moduli space of framed flags of sheaves is an irreducible, nonsingular variety carrying a holomorphic pre-symplectic form.