An introduction to motivic Hall algebras
By T. Bridgeland. 2010
126 citations recorded by the source corpus.
We give an introduction to Joyce's construction of the motivic Hall algebra of coherent sheaves on a variety M. When M is a Calabi-Yau threefold we define a semi-classical integration map from a Poisson subalgebra of this Hall algebra to the ring of functions on a symplectic torus. This material will be used in arxiv:1002.4374 to prove some basic properties of Donaldson-Thomas curve-counting invariants on Calabi-Yau threefolds.
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/3000f91958653acd479dd6c669b7743cf7b89a1c
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In Discrete Mathematics and Combinatorics
In Geometry and Topology
- T. Bridgeland
- Yukinobu Toda
- Emanuele Macrì
- Arend Bayer
- Alexander Kuznetsov
- P. Stellari
- D. Joyce
- D. Huybrechts
In Mathematical Physics
- T. Bridgeland
- Yukinobu Toda
- Emanuele Macrì
- Arend Bayer
- D. Joyce
- Chunyi Li
- Benjamin Schmidt
- P. Stellari
Citations in the corpus
- Scattering diagrams, Hall algebras and stability conditions (2016, methodology): “For the most general and abstract form of our result this is defined using the motivic Hall algebra [2, 10, 12, 16] of the category of representations of (Q, I).”