Theta functions and projective structures
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909406258528256 |
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| author | Biswas, Indranil Ghigi, Alessandro Vai, Luca |
| author_facet | Biswas, Indranil Ghigi, Alessandro Vai, Luca |
| contents | Given a compact Riemann surface $X$, we consider the line, in the space of sections of $2Θ$ on $J^0(X)$, orthogonal to all the sections that vanish at the origin. This line produces a natural meromorphic bidifferential on $X\times X$ with a pole of order two on the diagonal. This bidifferential is extensively investigated. In particular we show that it produces a projective structure on $X$ which is different from the standard ones. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_16037 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Theta functions and projective structures Biswas, Indranil Ghigi, Alessandro Vai, Luca Algebraic Geometry Complex Variables 14H10, 14H42, 14K25, 53B10 Given a compact Riemann surface $X$, we consider the line, in the space of sections of $2Θ$ on $J^0(X)$, orthogonal to all the sections that vanish at the origin. This line produces a natural meromorphic bidifferential on $X\times X$ with a pole of order two on the diagonal. This bidifferential is extensively investigated. In particular we show that it produces a projective structure on $X$ which is different from the standard ones. |
| title | Theta functions and projective structures |
| topic | Algebraic Geometry Complex Variables 14H10, 14H42, 14K25, 53B10 |
| url | https://arxiv.org/abs/2401.16037 |