Factorial threefolds and Shokurov vanishing

2004/10/10 by Cheltsov, Ivan
#14J17 #14J30 #14M10 #Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0410252

Abstract

We prove the factoriality of the following nodal threefolds: a complete intersection of hypersurfaces F and G⊂ℙ⁵ of degree n and k respectively, where G is smooth, |Sing(F∩ G)|\leqslant(n+k-2)(n-1)/5, n\geqslant k; a double cover of a smooth hypersurface F⊂ℙ⁴ of degree n branched over a surface that is cut out on F by a hypersurface G of degree 2r\geqslant n, and |Sing(F∩ G)|\leqslant(2r+n-2)r/4.

Related

• Factoriality of complete intersection threefolds
• On factoriality of nodal threefolds
• Points in projective spaces and applications
• Factorial threefold hypersurfaces
• Factorial hypersurfaces in P⁴ with nodes