Non-linear bi-algebraic curves and surfaces in moduli spaces of Abelian differentials
| Autor: | Deroin, Bertrand, Matheus, Carlos |
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| Rok vydání: | 2023 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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. $10$. Comment: 8 pages, final version (based on the referee report), to appear in C. R. Math. Acad. Sci. Paris |
| Databáze: | arXiv |
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