## Brini, Andrea and Cavalieri, Renzo - Crepant resolutions and open strings II

epiga:3879 - Épijournal de Géométrie Algébrique, July 6, 2018, Volume 2
Crepant resolutions and open strings II

Authors: Brini, Andrea and Cavalieri, Renzo

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.

Volume: Volume 2
Published on: July 6, 2018
Submitted on: August 25, 2017
Keywords: Mathematics - Algebraic Geometry,14N35