<i>K</i>-Theoretic Generalized Donaldson–Thomas Invariants

Kiem, Young-Hoon; Savvas, Michail

doi:10.1093/imrn/rnaa097

Cited by 6 publications

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“…In [KS21], the results of [KLS17] and the present paper are refined to define a virtual structure sheaf and a corresponding K -theoretic generalized DTK invariant.…”

Section: Donaldson–thomas Invariants Of Derived Objectsmentioning

confidence: 99%

Intrinsic Stabilizer Reduction and Generalized Donaldson–thomas Invariants

Savvas

2023

J. Inst. Math. Jussieu

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Let $\sigma $ be a stability condition on the bounded derived category $D^b({\mathop{\mathrm {Coh}}\nolimits } W)$ of a Calabi–Yau threefold W and $\mathcal {M}$ a moduli stack parametrizing $\sigma $ -semistable objects of fixed topological type. We define generalized Donaldson–Thomas invariants which act as virtual counts of objects in $\mathcal {M}$ , 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 $\widetilde {\mathcal {M}}^{\mathbb {C}^{\ast }}$ , called the $\mathbb {C}^{\ast }$ -rigidified intrinsic stabilizer reduction of $\mathcal {M}$ , 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 $[\widetilde {\mathcal {M}}]^{\mathrm {vir}} \in A_0(\widetilde {\mathcal {M}})$ . This stays invariant under deformations of the complex structure of W. Applications include Bridgeland stability, polynomial stability, Gieseker and slope stability.

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“…In [KS21], the results of [KLS17] and the present paper are refined to define a virtual structure sheaf and a corresponding K -theoretic generalized DTK invariant.…”

Section: Donaldson–thomas Invariants Of Derived Objectsmentioning

confidence: 99%