Abelian Quiver Invariants and Marginal Wall-Crossing

@article{Mozgovoy2012AbelianQI,
  title={Abelian Quiver Invariants and Marginal Wall-Crossing},
  author={Sergey Mozgovoy and Markus Reineke},
  journal={Letters in Mathematical Physics},
  year={2012},
  volume={104},
  pages={495-525}
}
We prove the equivalence of (a slightly modified version of) the wall-crossing formula of Manschot, Pioline and Sen and the wall-crossing formula of Kontsevich and Soibelman. The former involves abelian analogues of the motivic Donaldson–Thomas type invariants of quivers with stability introduced by Kontsevich and Soibelman, for which we derive positivity and geometricity properties. 
Block–Göttsche invariants from wall-crossing
We show how some of the refined tropical counts of Block and Göttsche emerge from the wall-crossing formalism. This leads naturally to a definition of a class of putative $q$-deformed Gromov–WittenExpand
Quiver moduli and small desingularizations of some GIT quotients
We construct small desingularizations of moduli spaces of semistable quiver representations for indivisible dimension vectors using deformations of stabilites and a dimension estimate for nullcones.Expand
The Coulomb Branch Formula for Quiver Moduli Spaces
In recent series of works, by translating properties of multi-centered supersymmetric black holes into the language of quiver representations, we proposed a formula that expresses the Hodge numbersExpand
Corfu lectures on wall-crossing, multi-centered black holes, and quiver invariants
The BPS state spectrum in four-dimensional gauge theories or string vacua with N=2 supersymmetries is well known to depend on the values of the parameters or moduli at spatial infinity. The BPS indexExpand
Quiver indices and Abelianization from Jeffrey-Kirwan residues
Abstract In quiver quantum mechanics with 4 supercharges, supersymmetric ground states are known to be in one-to-one correspondence with Dolbeault cohomology classes on the moduli space of stableExpand
Quiver invariants from Jeffrey-Kirwan residues
In quiver quantum mechanics with 4 supercharges, supersymmetric ground states are known to be in one-to-one correspondence with Dolbeault cohomology classes on the moduli space of stable quiverExpand
On the Coulomb and Higgs branch formulae for multi-centered black holes and quiver invariants
A bstractIn previous work we have shown that the equivariant index of multi-centered $ \mathcal{N}=2 $ black holes localizes on collinear configurations along a fixed axis. Here we provide a generalExpand
Line defects, tropicalization, and multi-centered quiver quantum mechanics
A bstractWe study BPS line defects in N$$ \mathcal{N} $$ = 2 supersymmetric four-dimensional field theories. We focus on theories of “quiver type,” those for which the BPS particle spectrum can beExpand
Tree structures in the geometric representation theory of quivers
One of the major goals in the representation theory of quivers is the classification of isomorphism classes of representations of arbitrary quivers and the homomorphism spaces between them. WhenceExpand

References

SHOWING 1-10 OF 23 REFERENCES
Cohomology of quiver moduli, functional equations, and integrality of Donaldson–Thomas type invariants
Abstract A system of functional equations relating the Euler characteristics of moduli spaces of stable representations of quivers and the Euler characteristics of (Hilbert-scheme-type) framedExpand
Poisson automorphisms and quiver moduli
  • M. Reineke
  • Mathematics
  • Journal of the Institute of Mathematics of Jussieu
  • 2009
Abstract A factorization formula for certain automorphisms of a Poisson algebra associated with a quiver is proved, which involves framed versions of moduli spaces of quiver representations. ThisExpand
Refined GW/Kronecker correspondence
Gromov–Witten invariants of weighted projective planes and Euler characteristics of moduli spaces of representations of bipartite quivers are related via the tropical vertex, a group of formalExpand
Positivity for Kac polynomials and DT-invariants of quivers
We give a cohomological interpretation of both the Kac polynomial and the rened Donaldson-Thomas-invariants of quivers. This interpretation yields a proof of a conjecture of Kac from 1982 and gives aExpand
Equivalence of Three Wall Crossing Formulae
  • A. Sen
  • Mathematics, Physics
  • 2011
The wall crossing formula of Kontsevich and Soibelman gives an implicit relation between the BPS indices on two sides of the wall of marginal stability by equating two symplectomorphisms constructedExpand
Cohomological Hall algebra, exponential Hodge structures and motivic Donaldson-Thomas invariants
We define a new type of Hall algebras associated e.g. with quivers with polynomial potentials. The main difference with the conventional definition is that we use cohomology of the stack ofExpand
The tropical vertex
Elements of the tropical vertex group are formal families of symplectomorphisms of the 2-dimensional algebraic torus. We prove ordered product factorizations in the tropical vertex group areExpand
Absolutely indecomposable representations and Kac-Moody Lie algebras
A conjecture of Kac states that the polynomial counting the number of absolutely indecomposable representations of a quiver over a finite field with given dimension vector has positive coefficientsExpand
Smooth models of quiver moduli
For any moduli space of stable representations of quivers, certain smooth varieties, compactifying projective space fibrations over the moduli space, are constructed. The boundary of thisExpand
MPS degeneration formula for quiver moduli and refined GW/Kronecker correspondence
Motivated by string-theoretic arguments Manschot, Pioline and Sen discovered a new remarkable formula for the Poincare polynomial of a smooth compact moduli space of stable quiver representationsExpand
...
1
2
3
...