Donaldson–Thomas theory and resolutions of toric A-singularities

Abstract

We prove the crepant resolution conjecture for Donaldson-Thomas invariants of toric Calabi-Yau 3-orbifolds with transverse A-singularities.

On the Gromov–Witten/Donaldson–Thomas Correspondence and Ruan’s Conjecture for Calabi–Yau 3-Orbifolds

“…The proof of Theorem 3 is rather roundabout, and relies heavily on previous work. Essentially, Theorem 3 is the composition of three previous results: the open CRC of Brini-Cavalieri-Ross [BCR13], the GW/DT correspondence of Maulik-Oblomkov-Okounkov-Pandharipande [MOOP11], and the DT vertex CRC of the author [Ros14].…”

“…The first identity is an exercise in n-quotients. In particular, it follows easily from the discussion in Section 3.2 of [Ros14]. The second identity follows from the infinite wedge expression for the characters of the generalized symmetric group.…”

On the crepant resolution conjecture for Donaldson-Thomas invariants

“…In the case of transverse A-singuarities, this identity was proved by Jim Bryan in the appendix to [You10]. Shortly before the last version of the present paper appeared on the arxiv, a proof of (C1) in the toric case with A-singularities was given by Dustin Ross [Ros14].…”

Quasimaps and stable pairs

“…In the CY limit this is verified by Proposition 49 and therefore what follows will constitute a proof. An alternate proof by direct computation was given in [42].…”

“…comes from V Pairs,CY ( ) = ••• V orb CY ( )for some monomial ••• (see, e.g.,[42, Theorem 3.1]). Presumably this monomial is exactly the CY limit of R q ℭ…”