5 problems

Let $(P,\Xi)$ be a principally polarized abelian variety of dimension $p\geq 4$, and let $V_{inf,00}$ be the base locus of the linear system of quartic tangent cones at the origin…

Let $p\geqslant 2$ be a prime number and let $(S,N)$ be a $\mathbb{Z}_p^m$-action of signature $(0;p^{n+1})$, where $2\leqslant m\leqslant n-1$. For each subgroup $L\leqslant N$ wi…

Let $\mathcal{C}$ be a non-hyperelliptic curve, let $\operatorname{Jac}(\mathcal{C})$ be its Jacobian, let $\Sigma$ denote the relevant theta divisor, and let the basis $\wp$-funct…

Flynn's conjecture. There exists a constant $\kappa$, independent of $g$, such that for every $m\leq\kappa g$, there exists a hyperelliptic curve of genus $g$ over ${\mathbb Q}$ wi…

Let $\mathcal{C}_{\vec{\mathsf r},\vec{\mathsf s}}$ be a unibranch plane curve singularity, let $J(\mathcal{C}_{\vec{\mathsf r},\vec{\mathsf s}})$ be its Jacobian factor, and write…