Donaldson–Thomas invariants versus intersection cohomology of quiver moduli

By Sven Meinhardt, Markus Reineke. Journal für die Reine und Angewandte Mathematik, 2014

77 citations recorded by the source corpus.

Abstract The main result of this paper is the statement that the Hodge theoretic Donaldson–Thomas invariant for a quiver with zero potential and a generic stability condition agrees with the compactly supported intersection cohomology of the closure of the stable locus inside the associated coarse moduli space of semistable quiver representations. In fact, we prove an even stronger result relating the Donaldson–Thomas “function” to the intersection complex. The proof of our main result relies on a relative version of the integrality conjecture in Donaldson–Thomas theory. This will be the topic of the second part of the paper, where the relative integrality conjecture will be proven in the motivic context.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/5e2b5f6c3feabf9fa0fe76d9e4f6a8b68174cf7a

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Citations in the corpus

The integrality conjecture and the cohomology of preprojective stacks (2016, unknown): “t (Q) ⊗Hc(CPf·d−1,Q) vir . DT THEORY AND PREPROJECTIVE STACKS 13 Proof. The proof is contained in the proof of [5, Thm.A], but we recall it anyway, since it is short (after assuming the results of [14]). By [14, Prop.4.3] there is an equality in the Grothendieck group of mixed Hodge modules on M(Q)”
Cohomological χ–independence for moduli of one-dimensional sheaves and moduli of Higgs bundles (2020, methodology): “We refer to [10, 11, 13, 14, 35, 38, 39] for applications of such techniques in the study of quivers representations and Donaldson–Thomas theory.”