INTRINSIC STABILIZER REDUCTION AND GENERALIZED DONALDSON-THOMAS INVARIANTS (vol 22, pg 1987, 2023)

Let be a stability condition on the bounded derived category of a Calabi-Yau threefold W and a moduli stack parametrizing -semistable objects of fixed topological type. We define generalized Donaldson-Thomas invariants which act as virtual counts of objects in, fully generalizing the approach introduced by Kiem, Li and the author in the case of semistable sheaves. We construct an associated proper Deligne-Mumford stack, called the -rigidified intrinsic stabilizer reduction of, with an induced semiperfect obstruction theory of virtual dimension zero, and define the generalized Donaldson-Thomas invariant via Kirwan blowups to be the degree of the associated virtual cycle. This stays invariant under deformations of the complex structure of W. Applications include Bridgeland stability, polynomial stability, Gieseker and slope stability. © The Author(s), 2023. Published by Cambridge University Press.