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arXiv · 2002.08524

The Open Crepant Transformation Conjecture for Toric Calabi-Yau 3-Orbifolds

Song Yu
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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.

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Song Yu. 2025-05-13. The Open Crepant Transformation Conjecture for Toric Calabi-Yau 3-Orbifolds. https://doi.org/10.4310/jdg%2F1747062764

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