Cohomology of quiver moduli, functional equations, and integrality of Donaldson–Thomas type invariants
By Markus Reineke. Compositio Mathematica, 2009
97 citations recorded by the source corpus.
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) framed versions of quiver moduli is derived. This is applied to wall-crossing formulas for the Donaldson–Thomas type invariants of M. Kontsevich and Y. Soibelman, in particular confirming their integrality.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/a5001810857368bfd8746a8f26bcc0dad039c21a
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In Geometry and Topology
- Mark Gross
- M. Kontsevich
- R. Pandharipande
- Y. Soibelman
- Bernd S Siebert
- M. Abouzaid
- T. Bridgeland
- D. Auroux
In Mathematical Physics
- Mark Gross
- R. Pandharipande
- M. Kontsevich
- Y. Soibelman
- M. Abouzaid
- Bernd S Siebert
- T. Bridgeland
- D. Auroux
Citations in the corpus
- Quivers, curves, and the tropical vertex (2009, background): “he above conjecture specializes to the series (1.3) in the (ℓ 1,ℓ 2) = (3,3) case. The specialization of (1.4) to ℓ 1 = ℓ 2 was conjectured by Kontsevich (motivated by (1.3)) and proved by Reineke in [18]. The series (1.4) attached to the ray of slope 1 is not always a rational functional in the var”
- Cohomological Hall algebra, exponential Hodge structures and motivic Donaldson-Thomas invariants (2010, background): “can get further examples with non-zero potentials. One can easily write an explicit formula for the symplectomorphism Tin the case of a quiver with zero potential. This is a result of M. Reineke (see [49]). We give a sketch of the proof for completeness. Theorem 7. For a quiver Qwith incidence matri”