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arXiv · 1712.04027

Linear Equations in Singular Moduli

Yuri Bilu·Lars Kühne
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Abstract

We establish an effective version of the Andr\'e-Oort conjecture for linear subspaces of $Y(1)^n_{\mathbb{C}} \approx \mathbb{A}_{\mathbb{C}}^n$. Apart from the trivial examples provided by weakly special subvarieties, this yields the first algebraic subvarieties in a Shimura variety of dimension $> 1$ whose CM-points can be (theoretically) determined.

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Yuri Bilu, Lars Kühne. 2017-12-11. Linear Equations in Singular Moduli. https://arxiv.org/abs/1712.04027

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