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On motivic Joyce-Song formula for the Behrend function identities

Research paper by Yunfeng Jiang

Indexed on: 04 Feb '16Published on: 04 Feb '16Published in: Mathematics - Algebraic Geometry



Abstract

We prove the motivic version of Joyce-Song formula for the Behrend function identities proposed in \cite{Jiang2}. The main method we use is Nicaise's motivic integration for formal schemes and Cluckers-Loeser's motivic constructible functions. As an application we prove that there is a Poisson algebra homomorphism from the motivic Hall algebra of the abelian category of coherent sheaves on a Calabi-Yau threefold $Y$ to the motivic quantum torus of $Y$, thus generalizing the integration map of Joyce-Song in \cite{JS} and Bridgeland in \cite{Bridgeland10} to the motivic level. Such an integration map has applications in the wall crossing of motivic Donaldson-Thomas invariants.