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

Bertrand Deroin; Carlos Matheus

doi:10.5802/crmath.529

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

Titre traduit de la contribution: Courbes et surfaces bi-algébriques non-linéaires dans les espaces de modules de différentielles abéliennes

CY Cergy Paris Université

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Résumé

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 (*) is fulfilled. In this note, we construct a non-linear bi-algebraic curve, resp. surface, of Abelian differentials of genus 7, resp. 10.

Titre traduit de la contribution	Courbes et surfaces bi-algébriques non-linéaires dans les espaces de modules de différentielles abéliennes
langue originale	Anglais
Pages (de - à)	1691-1698
Nombre de pages	8
journal	Comptes Rendus Mathematique
Volume	361
Numéro de publication	G10
Les DOIs	https://doi.org/10.5802/crmath.529
état	Publié - 1 janv. 2023

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

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