Curve counting theories via stable objects II: DT/ncDT flop formula

Abstract

The goal of the present paper is to show the transformation formula of Donaldson-Thomas invariants on smooth projective Calabi-Yau 3-folds under birational transformations via categorical method. We also generalize the non-commutative Donaldson-Thomas invariants, introduced by B. Szendr{\H o}i in a local $(-1,-1)$-curve example, to an arbitrary flopping contraction from a smooth projective Calabi-Yau 3-fold. The transformation formula between such invariants and the usual Donaldson-Thomas invariants are also established. These formulas will be deduced from the wall-crossing formula in the space of weak stability conditions on the derived category.

50 pages

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Cited by in corpus (6)

• A Donaldson-Thomas crepant resolution conjecture on Calabi-Yau 4-folds
• Stable pairs on local K3 surfaces
• Curve counting invariants around the conifold point
• Gromov--Witten/Pandharipande--Thomas correspondence via conifold transitions
• Flops and Hilbert schemes of space curve singularities
• Stable pairs on nodal K3 fibrations