4 problems

Franchetta conjecture. Every locally complete family of hyperkähler varieties satisfies the Franchetta property. The property is known for some Fano varieties, but the source prese…

Let $\mathcal{F}$ be the moduli stack of a locally complete family of polarised hyperkähler varieties, and let $\mathcal{X}\to\mathcal{F}$ be its universal family. Let $T$ be any m…

Let $[(X,h)]\in {\mathscr U}^{il}_e(2n)$, where ${\mathscr U}^{il}_e(2n)$ is the open subset of the moduli space of polarized hyperkähler varieties of type $K3^{[n]}$ for which the…

Let $X$ and $B$ be smooth connected varieties, and let $f:X\to B$ be a smooth projective morphism such that a very general fiber of $f$ admits motivic $0$-multiplicativity. Assume…