Factorial threefolds and Shokurov vanishing

Details Factorial threefolds and Shokurov vanishing Factorial threefolds and Shokurov vanishing

2004-10-10

arxiv.org/abs/math/0410252v4

Mathematics

Algebraic Geometry

22 pages, extended version, to appear in Sbornik: Mathematics

Scientific paper

We prove the factoriality of the following nodal threefolds: a complete intersection of hypersurfaces $F$ and $G\subset\mathbb{P}^{5}$ of degree $n$ and $k$ respectively, where $G$ is smooth, $|\mathrm{Sing}(F\cap G)|\leqslant(n+k-2)(n-1)/5$, $n\geqslant k$; a double cover of a smooth hypersurface $F\subset\mathbb{P}^{4}$ of degree $n$ branched over a surface that is cut out on $F$ by a hypersurface $G$ of degree $2r\geqslant n$, and $|\mathrm{Sing}(F\cap G)|\leqslant(2r+n-2)r/4$.

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