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Double cubics and double quartics

Ivan Cheltsov
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Abstract

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.

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Ivan Cheltsov. 2005-06-14. Double cubics and double quartics. https://arxiv.org/abs/math/0410408

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