4 problems

Let $\pi:\mathcal{X}\to B$ be a Fano fibration and let $M$ range over the Manin components of $\operatorname{Sec}(\mathcal{X}/B)$, with degree tending to infinity. Stability conjec…

Let $\pi:\mathcal{X}\to B$ be a Fano fibration over an algebraically closed field $\kappa$ of characteristic $0$. Let $A$ be the affine space of section classes and let…

Let $\pi:\mathcal{X}\to B$ be a Fano fibration over an algebraically closed field $\kappa$ of characteristic $0$. Let $\mathcal{P}$ be the convex hull in $N_1(\mathcal{X})$ of all…

Geometric Manin's conjecture. Sections of Fano fibrations over any ground field are governed by two key principles: pathological families of sections are controlled by the Fujita i…