Abstract
In this paper we show that the moduli stacks of Bridgeland semistable objects on smooth projective 3-folds are quasi-proper algebraic stacks of finite type if they satisfy the Bogomolov–Gieseker (BG for short) inequality conjecture proposed by Bayer, Macrì and the second author. The key ingredients are the equivalent form of the BG inequality conjecture and its generalization to arbitrary very weak stability conditions. This result is applied to define Donaldson–Thomas invariants counting Bridgeland semistable objects on smooth projective Calabi–Yau 3-folds satisfying the BG inequality conjecture, for example on étale quotients of abelian 3-folds.
Funding source: Ministry of Education, Culture, Sports, Science, and Technology
Award Identifier / Grant number: 26287002
Funding statement: This work is supported by World Premier International Research Center Initiative (WPI initiative), MEXT, Japan. The second author is also supported by Grant-in Aid for Scientific Research grant (No. 26287002) from the Ministry of Education, Culture, Sports, Science and Technology, Japan.
Acknowledgements
The authors would like to thank the organizers of the workshop “Geometry From Stability Conditions” held on February 16–20, 2015, at the University of Warwick. We are especially grateful to the referee for pointing out several errors and also for giving useful comments that led to a substantial improvement of this paper.
References
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© 2019 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Limits in 𝒫ℳℱ of Teichmüller geodesics
- Rational connectivity and analytic contractibility
- Uniformization of p-adic curves via Higgs–de Rham flows
- Néron models of jacobians over base schemes of dimension greater than 1
- Cuspidal curves, minimal models and Zaidenberg’s finiteness conjecture
- Moduli of Bridgeland semistable objects on 3-folds and Donaldson–Thomas invariants
- ⌢𝒟-modules on rigid analytic spaces I
- Tilings of amenable groups
- Universal K-matrix for quantum symmetric pairs
Articles in the same Issue
- Frontmatter
- Limits in 𝒫ℳℱ of Teichmüller geodesics
- Rational connectivity and analytic contractibility
- Uniformization of p-adic curves via Higgs–de Rham flows
- Néron models of jacobians over base schemes of dimension greater than 1
- Cuspidal curves, minimal models and Zaidenberg’s finiteness conjecture
- Moduli of Bridgeland semistable objects on 3-folds and Donaldson–Thomas invariants
- ⌢𝒟-modules on rigid analytic spaces I
- Tilings of amenable groups
- Universal K-matrix for quantum symmetric pairs