Obstruction theory for moduli spaces of framed flags of sheaves on the projective plane

TL;DR

This paper refines previous results on the moduli space of framed flags of sheaves on the projective plane by establishing the existence of unobstructed points and a perfect obstruction theory for related quiver moduli spaces.

Contribution

It replaces a previous claim with a weaker one and extends results on stability chambers and obstruction theories in the context of quiver moduli spaces.

Findings

Existence of unobstructed points in quiver moduli space

Extension of stability chamber results

Establishment of a perfect obstruction theory

Abstract

In a previous paper, the first two named authors established an isomorphism between the moduli space of framed flags of sheaves on the projective plane and the moduli space of stable representations of a certain quiver. In the present note, we substitute one of the claims made, namely [5, Theorem 17], for a weaker claim regarding the existence of unobstructed points in the quiver moduli space. We also extend some of the results of the cited paper, concerning the maximal stability chamber within which the isomorphism mentioned holds, and the existence of a perfect obstruction theory for the quiver moduli space.