The Open Crepant Transformation Conjecture for Toric Calabi-Yau 3-Orbifolds
Abstract
We prove an open version of Ruan's Crepant Transformation Conjecture for toric Calabi-Yau 3-orbifolds, which is an identification of disk invariants of K-equivalent semi-projective toric Calabi-Yau 3-orbifolds relative to corresponding Lagrangian suborbifolds of Aganagic-Vafa type. Our main tool is a mirror theorem of Fang-Liu-Tseng that relates these disk invariants to local coordinates on the B-model mirror curves. Treating toric crepant transformations as wall-crossings in the GKZ secondary fan, we establish the identification of disk invariants through constructing a global family of mirror curves over charts of the secondary variety and understanding analytic continuation on local coordinates. Our work generalizes previous results of Brini-Cavalieri-Ross on disk invariants of threefold type-A singularities and of Ke-Zhou on crepant resolutions with effective outer branes.
Keywords
Cite
@article{arxiv.2002.08524,
title = {The Open Crepant Transformation Conjecture for Toric Calabi-Yau 3-Orbifolds},
author = {Song Yu},
journal= {arXiv preprint arXiv:2002.08524},
year = {2025}
}
Comments
33 pages, 9 figures