The Open Crepant Transformation Conjecture for Toric Calabi-Yau 3-Orbifolds
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arXiv
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| Format: | Preprint |
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2020
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| _version_ | 1866909607911227392 |
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| author | Yu, Song |
| author_facet | Yu, Song |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2002_08524 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | The Open Crepant Transformation Conjecture for Toric Calabi-Yau 3-Orbifolds Yu, Song Algebraic Geometry 14N35 (Primary), 14J33 (Secondary) 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. |
| title | The Open Crepant Transformation Conjecture for Toric Calabi-Yau 3-Orbifolds |
| topic | Algebraic Geometry 14N35 (Primary), 14J33 (Secondary) |
| url | https://arxiv.org/abs/2002.08524 |