4 problems

Let $n\geq 1$, let $\mathrm{Y}_2(1)$ be the target variety for the tuple-valued function $J$, and let $\mathrm{E}_J^n$ be its graph over $\mathbb{H}^n$. A variety…

Let $n\geq 1$ and let $V\subseteq\mathbb{C}^n\times\mathrm{Y}(1)^n$ be an algebraic variety. A point of $V$ is generic over a field $K$ if its transcendence degree over $K$ equals…

Let $n\geq 1$, let $\mathrm{Y}(1)$ denote the modular curve, and let … A variety in $\mathbb{C}^n\times\mathrm{Y}(1)^n$ is broad when every coordinate projection indexed by $\ell$…

Let $\operatorname{\mathbb{H}}$ be the complex upper half-plane, let $j:\operatorname{\mathbb{H}}\to\operatorname{\mathbb{C}}$ be the modular $j$-function, and let…