9 problems

Let $A$) be the Jacobian of a smooth genus-two curve, embedded by $|3\Theta|$ in $\check{\mathbb{P}}^8$, and let $\mathscr{C}_3=Z(F)$ be the unique cubic hypersurface singular alon…

Let $L\subseteq\mathbb{P}^n$ be a linear subspace of dimension $d$ not contained in any coordinate hyperplane, let $L^{-1}$ be its reciprocal linear space, and let…

Let $L\subseteq\mathbb{P}^n$ be a linear subspace of dimension $d$ not contained in any coordinate hyperplane, let $L^{-1}$ be its reciprocal linear space, and let…

Let $\mathcal P$ be a regular rational polypol, and let $F_{\mathcal P}(u,v)$ denote its associated dual period. Consider the holonomic system annihilating $F_{\mathcal P}$, and th…

The conjectural structure of the hypergeometric discriminant for type $B_n$. The hypergeometric discriminant of $\texttt{B}_n$ is given by the formal sum

Let $\mathsf{X}\subset\mathbb{P}(\mathsf{V})$ be a smooth projective variety whose Hodge conjecture is true, and let $\mathsf{Y}\subset\mathbb{P}(\mathsf{V}^{\ast})$ be its project…

Extreme-coefficient conjecture. The extreme coefficients are

Tropical bitangent correspondence conjecture. There are $k$ distinct $n$-tangent hyperplanes $H$ with $\operatorname{Trop}(H)=p$.

Let $X \subset \mathbb{P}^N$ be an irreducible, smooth, non-degenerate, projective variety. Write $X^*$ for its projective dual, and let $\operatorname{ord}(X)$ denote its order. S…