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arXiv · 1002.4372

An introduction to motivic Hall algebras

Tom Bridgeland
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Abstract

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.

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Tom Bridgeland. 2010-02-23. An introduction to motivic Hall algebras. https://arxiv.org/abs/1002.4372

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