7 papers
Nilpotent quiver varieties with multiplicities and symmetrisable crystals
Victoria Hoskins, Joshua Jackson, Tanguy Vernet
We construct analogues of Nakajima's nilpotent quiver varieties for quivers with multiplicities, by developing new stability conditions for framed nilpotent quiver representations…
Moduli spaces of representations of quivers with multiplicities via non-reductive GIT
Victoria Hoskins, Joshua Jackson, Tanguy Vernet
We construct new moduli spaces of quiver representations with multiplicities, i.e. over rings of truncated power series. This includes moduli of framed representations and analogue…
The worst destabilizing 1-parameter subgroup for toric rational curves with one unibranch singularity
Joshua Jackson, David Swinarski
Kempf proved that when a point is unstable in the sense of Geometric Invariant Theory, there is a ``worst'' destabilizing 1-parameter subgroup . It is natural to ask: what a…
Affine Non-Reductive GIT and moduli of representations of quivers with multiplicities
Eloise Hamilton, Victoria Hoskins, Joshua Jackson
We give an explicit approach to quotienting affine varieties by linear actions of linear algebraic groups with graded unipotent radical, using results from projective Non-Reductive…
Quotients by Parabolic Groups and Moduli Spaces of Unstable Objects
Victoria Hoskins, Joshua Jackson
Motivated by constructing moduli spaces of unstable objects, we use new ideas in non-reductive GIT to construct quotients by parabolic group actions. For moduli problems with semis…
Moduli Spaces of Unstable Objects: Sheaves of Harder-Narasimhan Length 2
Joshua Jackson
Given a moduli problem posed using Geometric Invariant Theory, one can use Non-Reductive Geometric Invariant Theory to quotient unstable HKKN strata and construct 'moduli spaces of…
Variation of Non-reductive Geometric Invariant Theory
Gergely Bérczi, Joshua Jackson, Frances Kirwan
The wall-and-chamber structure of the dependence of the reductive GIT quotient on the choice of linearisation is well known. In this article, we first give a brief survey of recent…