Projective structures and Hodge theory
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909252074864640 |
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| author | Causin, Andrea Pirola, Gian Pietro |
| author_facet | Causin, Andrea Pirola, Gian Pietro |
| contents | Every compact Riemann surface $X$ admits a natural projective structure $p_u$ as a consequence of the uniformization theorem. In this work we describe the construction of another natural projective structure on $X$, namely the Hodge projective structure $p_h$, related to the second fundamental form of the period map. We then describe how projective structures correspond to $(1,1)$-differential forms on the moduli space of projective curves and, from this correspondence, we deduce that $p_u$ and $p_h$ are not the same structure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_18122 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Projective structures and Hodge theory Causin, Andrea Pirola, Gian Pietro Algebraic Geometry Differential Geometry 14H10, 53B10, 14K20, 14H40 Every compact Riemann surface $X$ admits a natural projective structure $p_u$ as a consequence of the uniformization theorem. In this work we describe the construction of another natural projective structure on $X$, namely the Hodge projective structure $p_h$, related to the second fundamental form of the period map. We then describe how projective structures correspond to $(1,1)$-differential forms on the moduli space of projective curves and, from this correspondence, we deduce that $p_u$ and $p_h$ are not the same structure. |
| title | Projective structures and Hodge theory |
| topic | Algebraic Geometry Differential Geometry 14H10, 53B10, 14K20, 14H40 |
| url | https://arxiv.org/abs/2405.18122 |