18 citations · 46 across the 17 of their papers we have counts for
24 papers
Relative Geometric Invariant Theory: Reductive and Non-reductive
Eloise Hamilton, Victoria Hoskins, Joshua Jackson
We construct good quotients for equivariant actions of group homomorphisms on morphisms of schemes. Using Geometric Invariant Theory, we obtain explicit open semistable loci in the…
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…
Projectivity of good moduli spaces of vector bundles on stacky curves
Chiara Damiolini, Victoria Hoskins, Svetlana Makarova +1
Moduli of vector bundles on stacky curves behave similarly to moduli of vector bundles on curves, except there are additional numerical invariants giving many different notions of…
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…
Moduli spaces and geometric invariant theory: old and new perspectives
Victoria Hoskins
Many moduli spaces are constructed as quotients of group actions; this paper surveys the classical theory, as well as recent progress and applications. We review geometric invarian…
Projectivity and effective global generation of determinantal line bundles on quiver moduli
Pieter Belmans, Chiara Damiolini, Hans Franzen +3
We give a moduli-theoretic treatment of the existence and properties of moduli spaces of semistable quiver representations, avoiding methods from geometric invariant theory. Using…
Voevodsky motives of stacks of coherent sheaves on a curve
Victoria Hoskins, Simon Pepin Lehalleur
We prove formulae for the motives of stacks of coherent sheaves of fixed rank and degree over a smooth projective curve in Voevodsky's triangulated category of mixed motives with r…
Motivic mirror symmetry and -independence for Higgs bundles in arbitrary characteristic
Victoria Hoskins, Simon Pepin Lehalleur
We prove that the (twisted orbifold) motives of the moduli spaces of and -Higgs bundles of coprime rank and degree on a smooth projective curve over…
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…
Motives of moduli spaces of rank 3 vector bundles and Higgs bundles on a curve
Lie Fu, Victoria Hoskins, Simon Pepin Lehalleur
We prove formulas for the rational Chow motives of moduli spaces of semistable vector bundles and Higgs bundles of rank 3 and coprime degree on a smooth projective curve. Our appro…
Motives of moduli spaces of bundles on curves via variation of stability and flips
Lie Fu, Victoria Hoskins, Simon Pepin Lehalleur
We study the rational Chow motives of certain moduli spaces of vector bundles on a smooth projective curve with additional structure (such as a parabolic structure or Higgs field).…
On the Voevodsky motive of the moduli space of Higgs bundles on a curve
Victoria Hoskins, Simon Pepin Lehalleur
We study the motive of the moduli space of semistable Higgs bundles of coprime rank and degree on a smooth projective curve C over a field k under the assumption that C has a ratio…
Parallels between moduli of quiver representations and vector bundles over curves
Victoria Hoskins
This is a review article exploring similarities between moduli of quiver representations and moduli of vector bundles over a smooth projective curve. After describing the basic pro…
A formula for the Voevodsky motive of the moduli stack of vector bundles on a curve
Victoria Hoskins, Simon Pepin Lehalleur
We prove a formula for the motive of the stack of vector bundles of fixed rank and degree over a smooth projective curve in Voevodsky's triangulated category of mixed motives with…
Stratifying quotient stacks and moduli stacks
Gergely Bérczi, Victoria Hoskins, Frances Kirwan
Recent results in geometric invariant theory (GIT) for non-reductive linear algebraic group actions allow us to stratify quotient stacks of the form [X/H], where X is a projective…
On the Voevodsky motive of the moduli stack of vector bundles on a curve
Victoria Hoskins, Simon Pepin Lehalleur
We define and study the motive of the moduli stack of vector bundles of fixed rank and degree over a smooth projective curve in Voevodsky's category of motives. We prove that this…
Rational points of quiver moduli spaces
Victoria Hoskins, Florent Schaffhauser
For a perfect field , we study actions of the absolute Galois group of on the -valued points of moduli spaces of quiver representations over ; the fixed locus is…
Group actions on quiver varieties and applications
Victoria Hoskins, Florent Schaffhauser
We study algebraic actions of finite groups of quiver automorphisms on moduli spaces of quiver representations. We decompose the fixed loci using group cohomology and we give a mod…
Algebraic symplectic analogues of additive quotients
Brent Doran, Victoria Hoskins
Motivated by the study of hyperkahler structures in moduli problems and hyperkahler implosion, we initiate the study of non-reductive hyperkahler and algebraic symplectic quotients…
Stratifications for moduli of sheaves and moduli of quiver representations
Victoria Hoskins
We study the relationship between two stratifications on parameter spaces for coherent sheaves and for quiver representations: a stratification by Harder-Narasimhan types and a str…
Stratifications associated to reductive group actions on affine spaces
Victoria Hoskins
For a complex reductive group G acting linearly on a complex affine space V with respect to a character, we show two stratifications of V associated to this action (and a choice of…
Stratifications of parameter spaces for complexes by cohomology types
Victoria Hoskins
We study a collection of stability conditions (in the sense of Schmitt) for complexes of sheaves over a smooth complex projective variety indexed by a positive rational parameter.…
Quotients of unstable subvarieties and moduli spaces of sheaves of fixed Harder-Narasimhan type
Victoria Hoskins, Frances Kirwan
When a reductive group acts linearly on a complex projective scheme there is a stratification of into -invariant locally closed subschemes, with an open stratum $X^{…