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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2504.19098 |
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| _version_ | 1866915261976674304 |
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| author | Han, Jian |
| author_facet | Han, Jian |
| contents | This thesis studies Frobenius manifolds arising from extended deformations of complex structures on compact Calabi-Yau manifolds, following the construction by Sergey Barannikov and Maxim Kontsevich. The work is based on the investigation of formal moduli spaces of solutions to the Maurer-Cartan equations modulo gauge equivalence. We provide a foundational overview of deformation theory from the perspective of differential geometry and prove the equivalence between gauge-equivalent deformations and isomorphic deformations. Based on this framework, we construct a differential Gerstenhaber-Batalin-Vilkovisky (dGBV) algebra associated to the deformation of Calabi-Yau manifolds and then construct the corresponding Frobenius manifold. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_19098 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Construction of Formal Frobenius Manifold from Deformation of Complex Structure Han, Jian Algebraic Geometry Mathematical Physics 32G05 This thesis studies Frobenius manifolds arising from extended deformations of complex structures on compact Calabi-Yau manifolds, following the construction by Sergey Barannikov and Maxim Kontsevich. The work is based on the investigation of formal moduli spaces of solutions to the Maurer-Cartan equations modulo gauge equivalence. We provide a foundational overview of deformation theory from the perspective of differential geometry and prove the equivalence between gauge-equivalent deformations and isomorphic deformations. Based on this framework, we construct a differential Gerstenhaber-Batalin-Vilkovisky (dGBV) algebra associated to the deformation of Calabi-Yau manifolds and then construct the corresponding Frobenius manifold. |
| title | A Construction of Formal Frobenius Manifold from Deformation of Complex Structure |
| topic | Algebraic Geometry Mathematical Physics 32G05 |
| url | https://arxiv.org/abs/2504.19098 |