Deformed dimensional reduction

Davison, Ben¹ ; Pădurariu, Tudor²

¹ School of Mathematics, University of Edinburgh, Edinburgh, United Kingdom
² Department of Mathematics, Columbia University, New York, NY, United States

Geometry & topology, Tome 26 (2022) no. 2, pp. 721-776.

Résumé

Since its first use by Behrend, Bryan, and Szendrői in the computation of motivic Donaldson–Thomas (DT) invariants of ${\mathbb{𝔸}}_{ℂ}^3$, dimensional reduction has proved to be a crucial 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.

Détail

DOI : 10.2140/gt.2022.26.721

Keywords: Donaldson–Thomas invariants, quivers with potential

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