| Résume | Classically, Donaldson-Thomas invariants are integer valued invariants that virtually count stable coherent sheaves on Calabi-Yau threefolds. On a Calabi-Yau fourfold, higher obstructions prevent the existence of virtual fundamental classes in the sense of Behrend-Fantechi. Nevertheless, Borisov-Joyce (via derived differential geometry) and Oh-Thomas (via deformation theory) constructed virtual fundamental classes in this setting, modulo choices of orientations. We review their constructions and explain how to define naturally numerical, K-theoretic and torus-equivariant invariants. Finally we discuss how, conjecturally, DT/PT/GW/GV invariants are related to each other and show instances where the conjectures have been checked. This is based on joint work with Y. Cao and M. Kool. |
