  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. $10$.
