5 problems

Let $n$ be a positive integer. For coordinate projections $\mathrm{Pr}_{\mathbf{i}}$ onto any selected $\ell$ pairs of coordinates, call an algebraic set…

Let $f_1,\ldots,f_n$ be holomorphic functions satisfying, for every distinct $i,j\in\{1,\ldots,n\}$, $f_i\notin\mathbb{Q}f_j+\mathbb{C}$. Write $\mathbf{f}=(f_1,\ldots,f_n)$ and…

Let $X$ be a smooth connected algebraic variety over $\mathbb{C}$, with base point $b \in X(\mathbb{C})$. Let $\mathscr{H}_{\mathbb{Z}}$ be a $\mathbb{Z}$-variation of mixed Hodge…

Let $(S,\mathbb{V})$ be a $\mathbb{Z}$VMHS and let $Y\subset\widetilde S$ be an algebraic subvariety. Ax–Lindemann for $\mathbb{Z}$VMHS. The Zariski closure … is a bi-algebraic sub…

Let $(S,\mathbb{V})$ be a $\mathbb{Z}$VMHS, let $U\subset\widetilde S\times S$ be an algebraic subvariety, and let $W$ be an irreducible component of $U\cap\Delta$, where $\Delta$…