Remodeling Conjecture with Descendants
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908730921058304 |
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| author | Fang, Bohan Liu, Chiu-Chu Melissa Yu, Song Zong, Zhengyu |
| author_facet | Fang, Bohan Liu, Chiu-Chu Melissa Yu, Song Zong, Zhengyu |
| contents | We formulate and prove the Remodeling Conjecture with descendants, which is a version of all-genus equivariant descendant mirror symmetry for semi-projective toric Calabi-Yau 3-orbifolds with integral structures. We construct an isomorphism between the $K$-group of equivariant coherent sheaves on the toric Calabi-Yau 3-orbifold with support bounded in a direction and a certain integral relative first homology group of the equivariant mirror curve. Under this isomorphism, we prove the equivariant mirror symmetric Gamma conjecture which equates quantum cohomology central charges of coherent sheaves and oscillatory integrals along corresponding relative 1-cycles. As a consequence in the non-equivariant setting, we prove a conjecture of Hosono which equates central charges of compactly supported coherent sheaves and period integrals of integral 3-cycles on the Hori-Vafa mirror 3-fold. Furthermore, we establish a correspondence between all-genus equivariant descendant Gromov-Witten invariants with $K$-theoretic framings and oscillatory integrals (Laplace transforms) of the Chekhov-Eynard-Orantin topological recursion invariants along relative 1-cycles on the equivariant mirror curve. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_15696 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Remodeling Conjecture with Descendants Fang, Bohan Liu, Chiu-Chu Melissa Yu, Song Zong, Zhengyu Algebraic Geometry 14N35, 14J33 We formulate and prove the Remodeling Conjecture with descendants, which is a version of all-genus equivariant descendant mirror symmetry for semi-projective toric Calabi-Yau 3-orbifolds with integral structures. We construct an isomorphism between the $K$-group of equivariant coherent sheaves on the toric Calabi-Yau 3-orbifold with support bounded in a direction and a certain integral relative first homology group of the equivariant mirror curve. Under this isomorphism, we prove the equivariant mirror symmetric Gamma conjecture which equates quantum cohomology central charges of coherent sheaves and oscillatory integrals along corresponding relative 1-cycles. As a consequence in the non-equivariant setting, we prove a conjecture of Hosono which equates central charges of compactly supported coherent sheaves and period integrals of integral 3-cycles on the Hori-Vafa mirror 3-fold. Furthermore, we establish a correspondence between all-genus equivariant descendant Gromov-Witten invariants with $K$-theoretic framings and oscillatory integrals (Laplace transforms) of the Chekhov-Eynard-Orantin topological recursion invariants along relative 1-cycles on the equivariant mirror curve. |
| title | Remodeling Conjecture with Descendants |
| topic | Algebraic Geometry 14N35, 14J33 |
| url | https://arxiv.org/abs/2504.15696 |