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 (*) is fulfilled. In this note, we construct a non-linear bi-algebraic curve, resp. surface, of Abelian differentials of genus 7, resp. 10.
| Translated title of the contribution | Courbes et surfaces bi-algébriques non-linéaires dans les espaces de modules de différentielles abéliennes |
|---|---|
| Original language | English |
| Pages (from-to) | 1691-1698 |
| Number of pages | 8 |
| Journal | Comptes Rendus Mathematique |
| Volume | 361 |
| Issue number | G10 |
| DOIs | |
| Publication status | Published - 1 Jan 2023 |