Cohomological orientifold Donaldson-Thomas invariants as Chow groups

TL;DR

This paper links orientifold Donaldson-Thomas invariants of symmetric quivers with involution to Chow groups, providing geometric insights and computational tools for moduli spaces of stable self-dual quiver representations.

Contribution

It establishes a geometric interpretation of orientifold DT invariants as Chow groups and derives a cohomological wall-crossing formula for Hall modules.

Findings

Chow Betti numbers of moduli spaces can be computed numerically.

Isomorphism between cohomological invariants and Chow groups.

Derived a wall-crossing formula for Hall modules.

Abstract

We establish a geometric interpretation of orientifold Donaldson-Thomas invariants of $\sigma$-symmetric quivers with involution. More precisely, we prove that the cohomological orientifold Donaldson-Thomas invariant is isomorphic to the rational Chow group of the moduli space of $\sigma$-stable self-dual quiver representations. As an application we prove that the Chow Betti numbers of moduli spaces of stable $m$-tuples in classical Lie algebras can be computed numerically. We also prove a cohomological wall-crossing formula relating semistable Hall modules for different stabilities.