Geometry & Topology

Motivic Donaldson–Thomas invariants for the one-loop quiver with potential

Ben Davison and Sven Meinhardt

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We compute the motivic Donaldson–Thomas invariants of the one-loop quiver, with an arbitrary potential. This is the first computation of motivic Donaldson–Thomas invariants to use in an essential way the full machinery of μ̂–equivariant motives, for which we prove a dimensional reduction result similar to that of Behrend, Bryan and Szendrői in their study of degree-zero motivic Donaldson–Thomas invariants. Our result differs from theirs in that it involves nontrivial monodromy.

Article information

Geom. Topol., Volume 19, Number 5 (2015), 2535-2555.

Received: 30 January 2013
Revised: 26 August 2014
Accepted: 30 September 2014
First available in Project Euclid: 16 November 2017

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Primary: 14N35: Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants [See also 53D45]
Secondary: 14D23: Stacks and moduli problems

motivic Donaldson–Thomas theory vanishing cycles quivers


Davison, Ben; Meinhardt, Sven. Motivic Donaldson–Thomas invariants for the one-loop quiver with potential. Geom. Topol. 19 (2015), no. 5, 2535--2555. doi:10.2140/gt.2015.19.2535.

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