Non-linear bi-algebraic curves and surfaces in moduli spaces of Abelian differentials
The strata of the moduli spaces of Abelian differentials are non-homogenous spaces carrying natural bi-algebraic structures. Partly inspired by the case of homogenous spaces carrying bi-algebraic structures (such as torii, Abelian varieties and Shimura varieties), Klingler and Lerer recently showed...
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| Language: | English |
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Académie des sciences
2023-11-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.529/ |
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| author | Deroin, Bertrand Matheus, Carlos |
| author_facet | Deroin, Bertrand Matheus, Carlos |
| author_sort | Deroin, Bertrand |
| collection | DOAJ |
| description | The strata of the moduli spaces of Abelian differentials are non-homogenous spaces carrying natural bi-algebraic structures. Partly inspired by the case of homogenous spaces carrying bi-algebraic structures (such as torii, Abelian varieties and Shimura varieties), Klingler and Lerer recently showed that any bi-algebraic curve in a stratum of the moduli space of Abelian differentials is linear provided that the so-called condition $(\star )$ is fulfilled.In this note, we construct a non-linear bi-algebraic curve, resp. surface, of Abelian differentials of genus $7$, resp. $10$. |
| format | Article |
| id | doaj-art-92d06bf3bf524feda6f650f450d18bbc |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2023-11-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-92d06bf3bf524feda6f650f450d18bbc2025-02-07T11:11:48ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692023-11-01361G101691169810.5802/crmath.52910.5802/crmath.529Non-linear bi-algebraic curves and surfaces in moduli spaces of Abelian differentialsDeroin, Bertrand0Matheus, Carlos1CNRS & Université de Cergy-Pontoise (UMR CNRS 8088), 95302, Cergy-Pontoise, FranceCNRS & École Polytechnique (UMR CNRS 7640), 91128, Palaiseau, FranceThe strata of the moduli spaces of Abelian differentials are non-homogenous spaces carrying natural bi-algebraic structures. Partly inspired by the case of homogenous spaces carrying bi-algebraic structures (such as torii, Abelian varieties and Shimura varieties), Klingler and Lerer recently showed that any bi-algebraic curve in a stratum of the moduli space of Abelian differentials is linear provided that the so-called condition $(\star )$ is fulfilled.In this note, we construct a non-linear bi-algebraic curve, resp. surface, of Abelian differentials of genus $7$, resp. $10$.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.529/ |
| spellingShingle | Deroin, Bertrand Matheus, Carlos Non-linear bi-algebraic curves and surfaces in moduli spaces of Abelian differentials Comptes Rendus. Mathématique |
| title | Non-linear bi-algebraic curves and surfaces in moduli spaces of Abelian differentials |
| title_full | Non-linear bi-algebraic curves and surfaces in moduli spaces of Abelian differentials |
| title_fullStr | Non-linear bi-algebraic curves and surfaces in moduli spaces of Abelian differentials |
| title_full_unstemmed | Non-linear bi-algebraic curves and surfaces in moduli spaces of Abelian differentials |
| title_short | Non-linear bi-algebraic curves and surfaces in moduli spaces of Abelian differentials |
| title_sort | non linear bi algebraic curves and surfaces in moduli spaces of abelian differentials |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.529/ |
| work_keys_str_mv | AT deroinbertrand nonlinearbialgebraiccurvesandsurfacesinmodulispacesofabeliandifferentials AT matheuscarlos nonlinearbialgebraiccurvesandsurfacesinmodulispacesofabeliandifferentials |