Motivic DT-invariants for the one loop quiver with potential

Abstract

In this paper we compute the motivic Donaldson--Thomas invariants for the quiver with one loop and any potential. As the presence of arbitrary potentials requires the full machinery of \hat(μ)-equivariant motives, we give a detailed account of them. In particular, we will prove two results for the motivic vanishing cycle which might be of importance not only in Donaldson--Thomas theory.

30 pages

References in corpus (1)

• Proofs of the integral identity conjecture over algebraically closed fields

Cited by in corpus (6)

• The motivic Donaldson-Thomas invariants of (-2) curves
• On the motive of the nested Quot scheme of points on a curve
• The local motivic DT/PT correspondence
• A tropical motivic Fubini theorem with applications to Donaldson-Thomas theory
• Deformed dimensional reduction
• Motivic mirror symmetry and $\chi$-independence for Higgs bundles in arbitrary characteristic