Framed motivic Donaldson-Thomas invariants of small crepant resolutions
Abstract
For an arbitrary integer r≥ 1, we compute r-framed motivic PT and DT 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 theory, fit nicely in the current development of higher rank refined DT invariants.
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