Geodesic
Crepant resolutions and open strings II
Épijournal de Géométrie Algébrique, Tome 2 (2018)

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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. 
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     author = {Brini, Andrea and Cavalieri, Renzo},
     title = {Crepant resolutions and open strings {II}},
     journal = {\'Epijournal de G\'eom\'etrie Alg\'ebrique},
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     volume = {2},
     year = {2018},
     doi = {10.46298/epiga.2018.volume2.3879},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/epiga.2018.volume2.3879/}
}
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Brini, Andrea; Cavalieri, Renzo. Crepant resolutions and open strings II. Épijournal de Géométrie Algébrique, Tome 2 (2018). doi: 10.46298/epiga.2018.volume2.3879

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