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An introduction to motivic Hall algebras

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

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Publisher copy:
10.1016/j.aim.2011.09.003
Journal:
Advances in Mathematics More from this journal
Volume:
229
Issue:
1
Pages:
102-138
Publication date:
2012-01-15
DOI:
EISSN:
1090-2082
ISSN:
0001-8708
Language:
English
Keywords:
Pubs id:
pubs:306426
UUID:
uuid:0c094794-8ce9-4cb8-b756-21d426935ef8
Local pid:
pubs:306426
Source identifiers:
306426
Deposit date:
2012-12-20

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