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Points in projective spaces and applications

Ivan Cheltsov
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Abstract

We prove the factoriality of a nodal hypersurface in $\mathbb{P}^{4}$ of degree $d$ that has at most $2(d-1)^{2}/3$ singular points, and factoriality of a double cover of $\mathbb{P}^{3}$ branched over a nodal surface of degree $2r$ having less than $(2r-1)r$ singular points.

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Ivan Cheltsov. 2006-10-02. Points in projective spaces and applications. https://arxiv.org/abs/math/0511578

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