Brauer-Severi motives and Donaldson-Thomas invariants of quantized 3-folds

TL;DR

This paper uses motives of Brauer-Severi schemes related to superpotential algebras to compute motivic Donaldson-Thomas invariants, providing evidence for conjectured formulas and confirming specific cases like the homogenised Weyl algebra.

Contribution

It introduces a method to compute motivic Donaldson-Thomas invariants using Brauer-Severi motives for Cayley-smooth algebras associated with superpotentials.

Findings

Confirmed the second term of the conjectured motivic series for the homogenised Weyl algebra.

Provided a new approach to test exponential conjectures for motivic Donaldson-Thomas invariants.

Abstract

Motives of Brauer-Severi schemes of Cayley-smooth algebras associated to homogeneous superpotentials are used to compute inductively the motivic Donaldson-Thomas invariants of the corresponding Jacobian algebras. This approach can be used to test the conjectural exponential expressions for these invariants, proposed in arXiv:1510.08116. As an example we confirm the second term of the conjectured expression for the motivic series of the homogenised Weyl algebra.