Meromorphic Projective Structures, Opers and Monodromy
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866915464497594368 |
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| author | Sérandour, Titouan |
| author_facet | Sérandour, Titouan |
| contents | The complex projective structures considered is this article are compact curves locally modeled on $\mathbb{CP}^1$. To such a geometric object, modulo marked isomorphism, the monodromy map associates an algebraic one: a representation of its fundamental group into $\operatorname{PGL}(2,\mathbb{C})$, modulo conjugacy. This correspondence is neither surjective nor injective. Nonetheless, it is a local diffeomorphism [Hejhal, 1975]. We generalize this theorem to projective structures admitting poles (without apparent singularity and with fixed residues): the corresponding monodromy map (including Stokes data) is a local biholomorphism. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_02203 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Meromorphic Projective Structures, Opers and Monodromy Sérandour, Titouan Differential Geometry Algebraic Geometry Complex Variables 30Fxx, 34M40, 34M45 The complex projective structures considered is this article are compact curves locally modeled on $\mathbb{CP}^1$. To such a geometric object, modulo marked isomorphism, the monodromy map associates an algebraic one: a representation of its fundamental group into $\operatorname{PGL}(2,\mathbb{C})$, modulo conjugacy. This correspondence is neither surjective nor injective. Nonetheless, it is a local diffeomorphism [Hejhal, 1975]. We generalize this theorem to projective structures admitting poles (without apparent singularity and with fixed residues): the corresponding monodromy map (including Stokes data) is a local biholomorphism. |
| title | Meromorphic Projective Structures, Opers and Monodromy |
| topic | Differential Geometry Algebraic Geometry Complex Variables 30Fxx, 34M40, 34M45 |
| url | https://arxiv.org/abs/2309.02203 |