Special subvarieties of non-arithmetic ball quotients and Hodge theory
نویسندگان
چکیده
Let $\Gamma \subset \mathrm{PU}(1,n)$ be a lattice and $S_\Gamma$ the associated ball quotient. We prove that, if contains infinitely many maximal complex totally geodesic subvarieties, then $\Gamma$ is arithmetic. also an Ax--Schanuel Conjecture for $S_\Gamma$, similar to one recently proven by Mok, Pila Tsimerman. One of main ingredients in proofs realise inside period domain polarised integral variations Hodge structure interpret subvarieties as unlikely intersections.
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ژورنال
عنوان ژورنال: Annals of Mathematics
سال: 2023
ISSN: ['1939-8980', '0003-486X']
DOI: https://doi.org/10.4007/annals.2023.197.1.3