Motivic DT-invariants for the one loop quiver with potential

TL;DR

This paper computes motivic Donaldson--Thomas invariants for a one-loop quiver with any potential, utilizing advanced motivic machinery and providing detailed accounts of equivariant motives and motivic vanishing cycles.

Contribution

It introduces a comprehensive computation of motivic DT-invariants for the one-loop quiver with arbitrary potential, expanding the theoretical framework.

Findings

Explicit formulas for motivic DT-invariants with arbitrary potentials

Development of techniques for quivariant motives in this context

Results on motivic vanishing cycles relevant beyond DT theory

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(\mu)-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.