18 citations · 33 across the 14 of their papers we have counts for
20 papers
Vector fields and admissible embeddings for quiver moduli
Pieter Belmans, Ana-Maria Brecan, Hans Franzen +1
We introduce a double framing construction for moduli spaces of quiver representations. It allows us to reduce certain sheaf cohomology computations involving the universal represe…
Rigidity and Schofield's partial tilting conjecture for quiver moduli
Pieter Belmans, Ana-Maria Brecan, Hans Franzen +2
We explain how Teleman quantization can be applied to moduli spaces of quiver representations to compute the higher cohomology of the endomorphism bundle of the universal bundle. W…
On Chow rings of quiver moduli
Pieter Belmans, Hans Franzen
We describe the point class and Todd class in the Chow ring of a quiver moduli space, building on a result of Ellingsrud-Strømme. This, together with the presentation of the Chow r…
A Gelfand-MacPherson correspondence for quiver moduli
Hans Franzen
We show that a semi-stable moduli space of representations of an acyclic quiver can be identified with two GIT quotients by reductive groups. One of a quiver Grassmannian of a proj…
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…
Torus Actions on Quotients of Affine Spaces
Ana-Maria Brecan, Hans Franzen
We study the locus of fixed points of a torus action on a GIT quotient of a complex vector space by a reductive complex algebraic group which acts linearly. We show that, under the…
Tautological bases of CoHA modules
Hans Franzen, Sergey Mozgovoy
Given a quiver, we consider its cohomological Hall algebra (CoHA) as well as CoHA modules built of cohomology groups of non-commutative Hilbert schemes. We investigate cell decompo…
Weight Spaces and Attracting Sets for Torus Actions on Quiver Moduli
Magdalena Boos, Hans Franzen
We study torus actions on moduli spaces of quivers. First we give a description of the weight spaces of the induced action of the tangent space to a torus-fixed point. Then we focu…
Torus-Equivariant Chow Rings of Quiver Moduli
Hans Franzen
We compute rational equivariant Chow rings with respect to a torus of quiver moduli spaces. We derive a presentation in terms of generators and relations, use torus localization to…
On the Cohomological Hall Algebra of the Kronecker Quiver
Hans Franzen, Markus Reineke
We give a short introduction to Cohomological Hall algebras of quivers and describe the semistable Cohomological Hall algebra of central slope of the Kronecker quiver in terms of g…
Rationality of Rigid Quiver Grassmannians
Hans Franzen
We show that any quiver Grassmannian associated with a rigid representation of a quiver is a rational variety using torus localization techniques.
Cell decompositions and algebraicity of cohomology for quiver Grassmannians
Giovanni Cerulli Irelli, Francesco Esposito, Hans Franzen +1
We show that the cohomology ring of a quiver Grassmannian asssociated with a rigid quiver representation has property (S): there is no odd cohomology and the cycle map is an isomor…
Cohomology Rings of Moduli of Point Configurations on the Projective Line
Hans Franzen, Markus Reineke
We describe the Chow rings of moduli spaces of ordered configurations of points on the projective line for arbitrary (sufficiently generic) stabilities. As an application, we exhib…
The Value of the Kac Polynomial at One
Hans Franzen, Thorsten Weist
We establish a formula for the value of the Kac polynomial at one in terms of Kac polynomials, evaluated at one, of the universal (abelian) covering quiver by applying torus locali…
Cohomological orientifold Donaldson-Thomas invariants as Chow groups
Hans Franzen, Matthew B. Young
We establish a geometric interpretation of orientifold Donaldson-Thomas invariants of -symmetric quivers with involution. More precisely, we prove that the cohomological orienti…
Semi-Stable Chow-Hall Algebras of Quivers and Quantized Donaldson-Thomas Invariants
H. Franzen, M. Reineke
The semi-stable ChowHa of a quiver with stability is defined as an analog of the Cohomological Hall algebra of Kontsevich and Soibelman via convolution in equivariant Chow groups o…
Non-Schurian indecomposables via intersection theory
Hans Franzen, Thorsten Weist
For an acyclic quiver with three vertices, we consider the canonical decomposition of a non-Schurian root and associate certain representations of a generalized Kronecker quiver. T…
On the Semi-Stable CoHa and its Modules Arising from Smooth Models
Hans Franzen
We study a variant of the semi-stable Cohomological Hall algebra which we construct using equivariant Chow groups. This algebra, we call it the semi-stable ChowHa, arises as a quot…
On Cohomology Rings of Non-Commutative Hilbert Schemes and CoHa-Modules
Hans Franzen
We prove that Chow groups of certain non-commutative Hilbert schemes have a basis consisting of monomials in Chern classes of the universal bundle. Furthermore, we realize the coho…
Chow Rings of Fine Quiver Moduli are Tautologically Presented
Hans Franzen
A result of A. King and C. Walter asserts that the Chow ring of a fine quiver moduli space is generated by the Chern classes of universal bundles if the quiver is acyclic. We will…