5 problems

Morrison's conjecture. For suitable $m$, the polarised projective bundle $(\mathbb P(E),L_m^{\otimes k})$ is Chow stable for $k\gg 0$.

Let $W$ be a rational Weierstrass fibration, let $X$ be its minimal resolution, and let $H$ be an arbitrary ample line bundle. Miranda's conjecture. The pair $(W,H)$ is asymptotica…

Conjectured equivalence. The two conditions—existence of a J-balanced metric and Chow stability of $|L_2|$—should be equivalent.

Let $X\subset\mathbb{P}^n$ be a complex irreducible smooth variety, and let $T\mathbb{P}^n_{|X}$ denote the restriction to $X$ of the tangent bundle of $\mathbb{P}^n$. Stability is…

Let $W$ be the ring of Witt vectors, with fraction field $K$ and residue field $k$. Let … be a smooth proper morphism where $X_W$ is an integral scheme, and let $D_W$ be an effecti…