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We construct relative moduli spaces of semistable pairs on a family of projective Deligne–Mumford stacks. We define moduli stacks of stable orbifold Pandharipande–Thomas pairs on stacks of expanded degenerations and pairs and then show they are separated and proper Deligne–Mumford stacks of finite type. As an application, we present the degeneration formula for the absolute and relative orbifold Pandharipande–Thomas invariants.

Relative Orbifold Pandharipande–Thomas Theory and the Degeneration Formula