Scattering diagrams, Hall algebras and stability conditions
By T. Bridgeland. Algebraic Geometry, 2016
122 citations recorded by the source corpus.
To any quiver with relations we associate a consistent scattering diagram taking values in the motivic Hall algebra of its category of representations. We show that the chamber structure of this scattering diagram coincides with the natural chamber structure in an open subset of the space of stability conditions on the associated triangulated category. In the three-dimensional Calabi-Yau situation, when the relations arise from a potential, we can apply an integration map to give a consistent scattering diagram taking values in a tropical vertex group.
Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/55effb88b9d130ad5912a2822bc1cf487c0a4af1
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Algebra and Number Theory
In Geometry and Topology
In Statistical and Nonlinear Physics
Citations in the corpus
- A survey on maximal green sequences (2019, unknown): “monet [30, 31]. When trying to compare the two proofs we are naturally lead to the problem of relating torsion classes to scattering diagrams. A first step towards its solution was taken by Bridgeland [10] who associates a scattering diagram (with values in a motivic Hall algebra) to each finite quive”
- Wall and chamber structure for finite-dimensional algebras (2018, methodology): “several conjectures on cluster algebras. However, the cluster scattering diagram is an intrinsically geometric object. Therefore, taking an algebraic approach to the problem, Bridgeland introduces in [8] the algebraic scattering diagram and shows that both scattering diagrams are isomorphic if the a”