Motivic invariants of quivers via dimensional reduction

Abstract

We provide a reduction formula for the motivic Donaldson–Thomas invariants associated with a quiver with superpotential. The method is valid provided the superpotential has a linear factor, it allows us to compute virtual motives in terms of ordinary motivic classes of simpler quiver varieties. We outline an application, giving explicit formulas for the motivic Donaldson–Thomas invariants of the orbifolds $${[\mathbb{C} \times \mathbb{C}^2/\mathbb{Z}_n]}$$ .