Twisted Sectors in Calabi-Yau Type Fermat Polynomial Singularities and Automorphic Forms
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arXiv
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866917316635131904 |
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| author | Zhang, Dingxin Zhou, Jie |
| author_facet | Zhang, Dingxin Zhou, Jie |
| contents | We study one-parameter deformations of Calabi-Yau type Fermat polynomial singularities along degree-one directions. We show that twisted sectors in the vanishing cohomology are components of automorphic forms for certain triangular groups. We prove consequentially that genus zero Gromov-Witten generating series of the corresponding Fermat Calabi-Yau varieties are components of automorphic forms. The main tools we use are mixed Hodge structures for quasi-homogeneous polynomial singularities, Riemann-Hilbert correspondence, and genus zero mirror symmetry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2112_07182 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Twisted Sectors in Calabi-Yau Type Fermat Polynomial Singularities and Automorphic Forms Zhang, Dingxin Zhou, Jie Algebraic Geometry Mathematical Physics Classical Analysis and ODEs We study one-parameter deformations of Calabi-Yau type Fermat polynomial singularities along degree-one directions. We show that twisted sectors in the vanishing cohomology are components of automorphic forms for certain triangular groups. We prove consequentially that genus zero Gromov-Witten generating series of the corresponding Fermat Calabi-Yau varieties are components of automorphic forms. The main tools we use are mixed Hodge structures for quasi-homogeneous polynomial singularities, Riemann-Hilbert correspondence, and genus zero mirror symmetry. |
| title | Twisted Sectors in Calabi-Yau Type Fermat Polynomial Singularities and Automorphic Forms |
| topic | Algebraic Geometry Mathematical Physics Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2112.07182 |