3 problems

Let $n\geq 3$ and let $X\subset \mathbb P^{n+1}$ be a very general cubic hypersurface. Stable irrationality conjecture. $X$ is not stably rational. The conjecture asks whether the…

Let $A$ be a finite abelian group, let $F^c(A)$ be its free central extension, and let $V$ be a faithful linear representation of $F^c(A)$ over an algebraically closed field $k$. F…

Let $\pi \colon X \to S$ be an $n$-dimensional standard conic bundle with $n \ge 3$, and let $\Delta$ denote the discriminant divisor of $\pi$. Higher-dimensional discriminant conj…