On the generalised André–Pink–Zannier conjecture. by Richard, Rodolphe, Yafaev, Andrei

Subjects: “…Shimura varieties…”
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Non-linear bi-algebraic curves and surfaces in moduli spaces of Abelian differentials by Deroin, Bertrand, Matheus, Carlos

“…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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