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.

arXiv comment40 pages

References in corpus (17)

• 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
• Purity for graded potentials and quantum cluster positivity
• The integrality conjecture and the cohomology of preprojective stacks
• Derived Kn"orrer periodicity and Orlov's theorem for gauged Landau-Ginzburg models
• Proofs of the integral identity conjecture over algebraically closed fields
• The motivic Donaldson-Thomas invariants of (-2) curves
• Donaldson-Thomas theory for categories of homological dimension one with potential
• Cohomological Donaldson-Thomas theory of a quiver with potential and quantum enveloping algebras
• K-theoretic Hall algebras for quivers with potential
• Motivic DT-invariants for the one loop quiver with potential
• The local motivic DT/PT correspondence
• Moduli spaces, indecomposable objects and potentials over a finite field
• A tropical motivic Fubini theorem with applications to Donaldson-Thomas theory
• Refined invariants of finite-dimensional Jacobi algebras
• Brauer-Severi motives and Donaldson-Thomas invariants of quantized 3-folds

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