Non-linear bi-algebraic curves and surfaces in moduli spaces of Abelian differentials

Bertrand Deroin; Carlos Matheus

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arXiv · 2303.00642

Non-linear bi-algebraic curves and surfaces in moduli spaces of Abelian differentials

Bertrand Deroin·Carlos Matheus

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Abstract

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. $10$.

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Bertrand Deroin, Carlos Matheus. 2023-03-01. Non-linear bi-algebraic curves and surfaces in moduli spaces of Abelian differentials. https://arxiv.org/abs/2303.00642

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