Cosection Localization and Vanishing for Virtual Fundamental Classes of D-Manifolds
arXiv:2007.14023 · doi:10.1016/j.aim.2022.108232
Abstract
We establish cosection localization and vanishing results for virtual fundamental classes of derived manifolds, combining the theory of derived differential geometry by Joyce with the theory of cosection localization by Kiem-Li. As an application, we show that the stable pair invariants of hyperkähler fourfolds, defined by Cao-Maulik-Toda, are zero.
arXiv comment29 pages; results and exposition improved. Published version
References in corpus (13)
- The intrinsic normal cone
- Virtual fundamental classes for moduli spaces of sheaves on Calabi-Yau four-folds
- Zero-dimensional Donaldson-Thomas invariants of Calabi-Yau 4-folds
- Orientability of moduli spaces of Spin(7)-instantons and coherent sheaves on Calabi-Yau 4-folds
- -theoretic DT/PT correspondence for toric Calabi-Yau 4-folds
- Genus zero Gopakumar-Vafa type invariants for Calabi-Yau 4-folds
- Donaldson-Thomas theory for Calabi-Yau 4-folds
- Curve counting and DT/PT correspondence for Calabi-Yau 4-folds
- Counting sheaves on Calabi-Yau 4-folds, I
- Gromov-Witten invariants of varieties with holomorphic 2-forms
- Curve counting via stable objects in derived categories of Calabi-Yau 4-folds
- Genus zero Gopakumar-Vafa type invariants for Calabi-Yau 4-folds II: Fano 3-folds
- Quantum singularity theory via cosection localization