3 problems

Let $\mathcal{H}=\{H_i\}$ be a hyperplane arrangement in $\mathbb{CP}^n$, let $C^{\circ}$ be its stable cone, and let $Q$ be the associated quadratic form. For a weight vector…

Assume Setup, with $X$ a Fano manifold and $\omega \in c_1(X)$. Let $v \colon P \to \mathbb{R}_{>0}$ be a weight, let $\mathscr{V}$ be a canonical extension sheaf with extension cl…

Let $S$ be a surface of general type whose Picard scheme is smooth. A version of the Miyaoka–Yau inequality should hold for $S$. Parshin's conjecture. If the Picard scheme of a giv…