Crepant resolutions and open strings II

Andrea Brini (1) , Renzo Cavalieri (2)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier
2 CSU-Math

We recently formulated a number of Crepant Resolution Conjectures (CRC) for open Gromov-Witten invariants of Aganagic-Vafa Lagrangian branes and verified them for the family of threefold type A-singularities. In this paper we enlarge the body of evidence in favor of our open CRCs, along two different strands. In one direction, we consider non-hard Lefschetz targets and verify the disk CRC for local weighted projective planes. In the other, we complete the proof of the quantized (all-genus) open CRC for hard Lefschetz toric Calabi-Yau three dimensional representations by a detailed study of the G-Hilb resolution of $[C^3/G]$ for $G=\mathbb{Z}_2 \times \mathbb{Z}_2$. Our results have implications for closed-string CRCs of Coates-Iritani-Tseng, Iritani, and Ruan for this class of examples.

Domaines: Géométrie algébrique [math.AG]

Andrea Brini, Renzo Cavalieri. Crepant resolutions and open strings II. 2014. ⟨hal-01116214⟩