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.
Coates, Tom; Iritani, Hiroshi, 2018, A Fock Sheaf For Givental Quantization, Kyoto Journal Of Mathematics, 58, 4, 10.1215/21562261-2017-0036.
Ke, Hua-Zhong; Zhou, Jian, 2014, Gauged Linear Sigma Model For Disc Invariants, Letters In Mathematical Physics, 105, 1, pp. 63-88, 10.1007/s11005-014-0730-1.
Ke, Hua-Zhong; Zhou, Jian, 2014, Quantum McKay Correspondence For Disc Invariants Of Toric Calabi-Yau 3-Orbifolds, Acta Mathematica Sinica, English Series, 31, 1, pp. 29-34, 10.1007/s10114-015-3281-1.
