Compact edges of a G2 multi-moment graph lift from the base via cohomological formulas, and in the toric case the loop closes exactly when the cohomological condition [ω]∪[F]=0 holds.
Altmann, The versal deformation of an isolated toric Gorenstein sing ularity, In- vent
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Cohomological lifting of multi-toric graphs
Compact edges of a G2 multi-moment graph lift from the base via cohomological formulas, and in the toric case the loop closes exactly when the cohomological condition [ω]∪[F]=0 holds.