Double cubics and double quartics

Details Double cubics and double quartics Double cubics and double quartics

2004-10-18

arxiv.org/abs/math/0410408v4

Mathematics

Algebraic Geometry

9 pages

Scientific paper

We study a double cover $\psi:X\to V\subset\mathbb{P}^{n}$ 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.

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