We study the Donaldson–Thomas type invariants for the Calabi–Yau threefold Deligne–Mumford stacks under flops. A crepant birational morphism between two smooth Calabi–Yau threefold Deligne–Mumford stacks is called an orbifold flop if the flopping locus is the quotient of weighted projective lines by a cyclic group action. We prove that the Donaldson–Thomas invariants are preserved under orbifold flops.
"Donaldson–Thomas invariants of Calabi–Yau orbifolds under flops." Illinois J. Math. 62 (1-4) 61 - 97, 2018. https://doi.org/10.1215/ijm/1552442657