3 problems

Let $\mathcal{M}^o$ be a finite-type algebraic $\mathbbm{k}$-stack underlying a $\mathbb{Q}$-Gorenstein faithfully flat affine family of $\mathbb{Q}$-Fano fibrations, equipped with…

Consider $T$-equivariant Fano fibrations $\pi\colon X\to Y$, fixing the multi-Hilbert function of $T\curvearrowright Y$ and the Hilbert polynomial of $-K_X$ on the fibers of $\pi$.…

Let $S$ be a finite type $\mathbbm{k}$-scheme and let $\pi\colon\mathcal{X}\to S$ be a $\mathbb{Q}$-Gorenstein family whose $h$-invariants and volumes are constant on closed fibers…