A degeneration formula of Donaldson-Thomas theory on local Calabi-Yau 4-folds

Abstract

We define relative Donaldson-Thomas invariants of local log Calabi-Yau 4-folds, under the assumption that the derived Hilbert scheme on the anti-canonical divisor is a derived critical locus. We prove a degeneration formula and apply it to compute zero dimensional invariants on $\mathbb{C}^4$ and on any local curve. This verifies a conjecture proposed by the first author and Kool.