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Linear Equations in Singular Moduli

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We establish an effective version of the André–Oort conjecture for linear subspaces of $Y(1)^n_{\mathbb{C}} \approx \mathbb{A}_{\mathbb{C}}^n$. This gives the first effective nontrivial results of André–Oort type for higher-dimensional varieties in… Click to show full abstract

We establish an effective version of the André–Oort conjecture for linear subspaces of $Y(1)^n_{\mathbb{C}} \approx \mathbb{A}_{\mathbb{C}}^n$. This gives the first effective nontrivial results of André–Oort type for higher-dimensional varieties in products of modular curves.

Keywords: equations singular; singular moduli; linear equations

Journal Title: International Mathematics Research Notices
Year Published: 2018

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