Smooth models of quiver moduli

By J. Engel, Markus Reineke. 2007

78 citations recorded by the source corpus.

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 this compactification is analyzed. Explicit formulas for the Betti numbers of the smooth models are derived. In the case of moduli of simple representations, explicit cell decompositions of the smooth models are constructed.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/a84ef4c906204f6f871a9f6ab96b3bf1bb1d9ad7

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Scattering diagrams, Hall algebras and stability conditions (2016, methodology): “When W = 0 and θ(d) = 0 this moduli space coincides with the smooth quiver moduli space of [5].”
Poisson automorphisms and quiver moduli (2008, methodology): “That this property applies to the generating series induced from the Harder–Narasimhan recursion follows from a formula for the Betti numbers of smooth models of [2]; this is explained in § 5.”
Cohomology of quiver moduli, functional equations, and integrality of Donaldson–Thomas type invariants (2009, methodology): “By [7], there exists a smooth complex variety M d,n(Q), called a smooth model for M sst d (Q), whose points parametrize equivalence classes of stable pairs as above.”
Quivers, curves, and the tropical vertex (2009, methodology): “o (0,1)- (semi)stability.QUIVERS, CURVES, AND THE TROPICAL VERTEX 11 2.4. Framing. Strictly semistable representations of Qm usually lead to singularities of the moduli space Mω m(d 1,d 2). Following [4], we introduce framing data to improve the moduli behaviour. We consider two types of framings fo”
Moduli of representations of quivers (2008, background): “The material of this section is contained in [19].”
A theory of generalized Donaldson–Thomas invariants (2008, methodology): “These quiver analogues of Mα,nstp (τ ′), P Iα,n(τ ′) are not new, similar things have been studied in quiver theory by Nakajima, Reineke, Szendrői and other authors for some years [24, 82–85, 88, 89, 99].”