An introduction to motivic Hall algebras

Details An introduction to motivic Hall algebras An introduction to motivic Hall algebras

2010-02-23

arxiv.org/abs/1002.4372v1

Mathematics

Algebraic Geometry

35 pages

Scientific paper

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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