Framed motivic Donaldson-Thomas invariants of small crepant resolutions

For an arbitrary integer r >= 1$r\ge 1$, we compute r-framed motivic DT and PT invariants of small crepant resolutions of toric Calabi-Yau 3-folds, establishing a higher rank version of the motivic DT/PT wall-crossing formula. This generalises the work of Morrison and Nagao. Our formulae, in particular their relationship with the r=1$r=1$ theory, fit nicely in the current development of higher rank refined DT invariants.

Automated summary

In this paper, we compute r-framed motivic DT and PT invariants of small crepant resolutions of toric Calabi-Yau 3-folds for an arbitrary integer r ≥ 1, establishing a higher rank version of the motivic DT/PT wall-crossing formula. This generalizes the work of Morrison and Nagao and shows the relationship between our formulae with r=1 theory, fitting nicely in the current development of higher rank refined DT invariants.