Wall-crossing of the motivic Donaldson-Thomas invariants

TL;DR

This paper investigates how motivic Donaldson-Thomas invariants change across walls in the stability space, proving a mutation-based wall-crossing formula for specific quivers with potentials.

Contribution

It introduces a new wall-crossing formula for motivic DT invariants under mutations for a class of quivers with potentials.

Findings

Proves a mutation-based wall-crossing formula for motivic DT invariants.

Establishes invariance properties under certain quiver mutations.

Advances understanding of motivic DT invariants in algebraic geometry.

Abstract

We study motivic Donaldson-Thomas invariants in the sense of Behrend-Bryan-Szendroi. A wall-crossing formula under a mutation is proved for a certain class of quivers with potentials.