An introduction to motivic Hall algebras

作者：Bridgeland Tom^*

来源：Advances in Mathematics, 2012, 229(1): 102-138.

DOI：10.1016/j.aim.2011.09.003

• Algebraic stacks
• Coherent sheaves
• Hall algebra
• Donaldson-Thomas invariants

We give an introduction to Joyce%26apos;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.

• 出版日期2012-1-15