5 problems

Let $(\mathbb{R}P^1)^3$ be the product of three real projective lines with the standard real structure, and let $\mathfrak{s}_{(\mathbb{R}P^1)^3}$ be the $Spin_3$-structure over…

Let $B_5\subset\mathbb P^6$ be the del Pezzo threefold, and let $H_{B_5}$ be a hyperplane section. For $i=1$ or $i=2$, take $D\in\lvert iH_{B_5}\rvert$. Vojta's conjecture. The int…

Let $X$ be a dPA$^q$-variety, meaning that $S^q(X)$ is a del Pezzo $q$-secant variety and the map $\widetilde{S}^q(X)\to S^q(X)$ is birational. Assume…

Let $S^q(X)$ denote the $q$-th secant variety of $X$. A del Pezzo $q$-secant variety is a $q$-secant variety of del Pezzo type, and a dPA$^q$-variety is a variety for which…

Effective anticanonical divisor conjecture. There is an effective $\mathbb{Q}$-divisor $D$ on $X$ such that