An introduction to motivic Hall algebras

Journal article

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 Bridgeland (2011) [3] to prove some basic properties of Donaldson-Thomas curve-counting invariants on Calabi-Yau threefolds. © 2011 Elsevier Inc..

Authors: Bridgeland, T

• Journal: Advances in Mathematics
• Volume: 229
• Issue: 1
• Pages: 102-138
• Publication date: 2012-01-15
• DOI: 10.1016/j.aim.2011.09.003
• EISSN: 1090-2082
• ISSN: 0001-8708
• Language: English
• Keywords: Algebraic stacks; Coherent sheaves; Hall algebra; Donaldson-Thomas invariants