Deformed dimensional reduction

Abstract

Since its first use by Behrend, Bryan, and Szendrői in the computation of motivic Donaldson-Thomas (DT) invariants of ${\mathbb{A}}_{\mathbb{C}}^3$, dimensional reduction has proved to be an important tool in motivic and cohomological DT theory. Inspired by a conjecture of Cazzaniga, Morrison, Pym, and Szendrői on motivic DT invariants, work of Dobrovolska, Ginzburg, and Travkin on exponential sums, and work of Orlov and Hirano on equivalences of categories of singularities, we generalize the dimensional reduction theorem in motivic and cohomological DT theory and use it to prove versions of the Cazzaniga-Morrison-Pym-Szendrői conjecture in these settings.

40 pages

References in corpus (5)

• Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
• Cohomological Hall algebra, exponential Hodge structures and motivic Donaldson-Thomas invariants
• The Grothendieck group of algebraic stacks
• K-theoretic Hall algebras for quivers with potential
• Moduli spaces, indecomposable objects and potentials over a finite field

Cited by in corpus (2)

• K-theoretic Hall algebras for quivers with potential
• BPS Lie algebras and the less perverse filtration on the preprojective CoHA