Andrea Brini ; Renzo Cavalieri - Crepant resolutions and open strings II

epiga:3879 - Épijournal de Géométrie Algébrique, July 6, 2018, Volume 2 - https://doi.org/10.46298/epiga.2018.volume2.3879
Crepant resolutions and open strings IIArticle

Authors: Andrea Brini ; Renzo Cavalieri

    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
    Accepted on: May 12, 2018
    Submitted on: August 25, 2017
    Keywords: Mathematics - Algebraic Geometry,14N35
    Funding:
      Source : OpenAIRE Graph
    • Tautological Intersection Theory on Moduli Spaces; Funder: National Science Foundation; Code: 1101549
    • Development of PEMD for Nuclear Coolant Systems; Funder: National Science Foundation; Code: 77777
    • FRG: Collaborative Research: Gromov-Witten Theory; Funder: National Science Foundation; Code: 1159964

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