Relative Orbifold Donaldson-Thomas Theory and the Degeneration Formula

Abstract

We generalize the notion of expanded degenerations and pairs for a simple degeneration or smooth pair to the case of smooth Deligne-Mumford stacks. We then define stable quotients on the classifying stacks of expanded degenerations and pairs and prove the properness of their moduli's. On 3-dimensional smooth projective DM stacks this leads to a definition of relative Donaldson-Thomas invariants and the associated degeneration formula.

59 pages. Final version

References in corpus (3)

• Moduli Spaces of Semistable Sheaves on Projective Deligne-Mumford Stacks
• Grothendieck Duality for Deligne-Mumford Stacks
• Riemann-Roch for Deligne-Mumford stacks

Cited by in corpus (2)

• Donaldson-Thomas theory of $[{\mathbb{C}}^2/{\mathbb{Z}}_{n+1}]\times {\mathbb{P}}^1$
• Gromov--Witten/Pandharipande--Thomas correspondence via conifold transitions