The Wirtinger-type integral for a genus two curve
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866918363239809024 |
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| author | Goto, Yoshiaki |
| author_facet | Goto, Yoshiaki |
| contents | The Wirtinger integral is one of the integral representations of the Gauss hypergeometric function. Its integrand can be regarded as a multivalued function on an elliptic curve. In this paper, we study an analogue of the Wirtinger integral on a hyperelliptic curve of genus two, introduced by Mizutani and Watanabe. We investigate the associated twisted homology and cohomology groups using the hyperelliptic involution and intersection forms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_00577 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Wirtinger-type integral for a genus two curve Goto, Yoshiaki Algebraic Geometry 33C99, 14H45, 55N25 The Wirtinger integral is one of the integral representations of the Gauss hypergeometric function. Its integrand can be regarded as a multivalued function on an elliptic curve. In this paper, we study an analogue of the Wirtinger integral on a hyperelliptic curve of genus two, introduced by Mizutani and Watanabe. We investigate the associated twisted homology and cohomology groups using the hyperelliptic involution and intersection forms. |
| title | The Wirtinger-type integral for a genus two curve |
| topic | Algebraic Geometry 33C99, 14H45, 55N25 |
| url | https://arxiv.org/abs/2603.00577 |