Double cubics and double quartics

الأصل · EN

We study a double cover ψ:X→ Vⁿ branched over a smooth divisor R⊂ V such that R is cut on V by a hypersurface of degree 2(n-deg(V)), where n 8 and V is a smooth hypersurface of degree 3 or 4. We prove that X is nonrational and birationally superrigid.