5 problems

Let $\mathcal{X}/C$ be an abelian scheme and suppose it does not admit an isotrivial abelian subscheme. If … then for some finite étale cover $C'\twoheadrightarrow C$, the…

Let $f:\mathcal{X}\to C$ be an abelian scheme, and suppose that the Hodge bundle $f_*\Omega^1_{\mathcal{X}/C}$ is non-nef. An isogeny-leaf factor conjecture predicts that this non-…

Let $f\colon S\to B$ be a fibred surface, meaning a fibration from a smooth projective surface $S$ to a smooth projective curve $B$, with general fibre of genus $g\geq 2$. Let…

Let ${\mathcal L}_1$ be a suborbifold in the moduli space of unit area Abelian differentials, or in the moduli space of unit area meromorphic quadratic differentials with at most s…

Let $X$ be a smooth projective variety and let $\{T_a\}$ be a basis of $H^*(X,\mathbb Q)$, with dual basis $T^a=g^{ab}T_b$ for the Poincaré pairing. Write…