Relative orbifold Pandharipande-Thomas theory and the degeneration formula

Abstract

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.

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• Gromov--Witten/Pandharipande--Thomas correspondence via conifold transitions
• The orbifold DT/PT vertex correspondence