Relative orbifold Pandharipande-Thomas theory and the degeneration formula
Yijie Lin
TL;DR
This paper develops a framework for orbifold Pandharipande-Thomas theory on stacks, constructing moduli spaces and deriving a degeneration formula for invariants, advancing enumerative geometry in orbifold settings.
Contribution
It introduces relative moduli spaces and stable pairs in orbifold settings, establishing properness and separation, and derives a degeneration formula for orbifold PT invariants.
Findings
Construction of relative moduli spaces of semistable pairs
Definition of stable orbifold PT pairs on stacks of expanded degenerations
Degeneration formula for orbifold PT invariants
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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