Double cubics and double quartics
Abstract
Description
We study a double cover $ψ:X\to V\subset\mathbb{P}^{n}$ branched over a smooth divisor $R\subset V$ such that $R$ is cut on $V$ by a hypersurface of degree $2(n-\mathrm{deg}(V))$, where $n\geqslant 8$ and $V$ is a smooth hypersurface of degree 3 or 4. We prove that $X$ is nonrational and birationally superrigid.
9 pages
9 pages