5 problems

Freitag's freeness conjecture. If the modular variety $(\mathcal D / \Gamma)^*$ is a weighted projective space, then there exists a weight $k_0$ and a multiplier system $v_0$ of we…

Let $S$ be a curve in an orthogonal modular variety, let $\mathcal{Z}(\gamma,-n)$ denote the corresponding special cycle for $\gamma\in V^{\vee}/V$ and $n\in -Q(\gamma)+\mathbb{Z}$…

Let $L=\Pi_{2,10}$ be the even unimodular lattice of signature $(2,10)$, let ${fam0 inerm O}^+(L)$ be the index-two subgroup of its orthogonal group acting on the ten-dimensional t…

Let $L=3U\oplus 2E_8(-1)\oplus A_2(-1)$ be the Beauville lattice of an O'Grady $10$-dimensional variety, let $h\in L$ be a polarisation, let $\mathcal M_h^0$ be a component of its…

Let $L$ be a lattice of signature $(2,n)$ with $n\ge 3$. Assume that the branch divisor of the modular variety $\mathcal F_L(\Gamma)$ has several components, and suppose that there…