Hall algebras and curve-counting invariants

Bridgeland, Tom

doi:10.1090/S0894-0347-2011-00701-7

Hall algebras and curve-counting invariants
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by Tom Bridgeland

J. Amer. Math. Soc. 24 (2011), 969-998

DOI: https://doi.org/10.1090/S0894-0347-2011-00701-7

Published electronically: April 6, 2011

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Abstract:

We use Joyce’s theory of motivic Hall algebras to prove that reduced Donaldson-Thomas curve-counting invariants on Calabi-Yau threefolds coincide with stable pair invariants and that the generating functions for these invariants are Laurent expansions of rational functions.

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