Factorial Nodal Threefolds in P 5
نویسنده
چکیده
In this paper we study a 3-fold X ⊂ P that is a complete intersection of two hypersurfaces Fn and Gk of degree n and k respectively such that n ≥ k and the only singularities of X are ordinary double points. The 3-fold X is called factorial if every surface in X is cut by a hypersurface in P. The factoriality of the 3-fold X is equivalent to a global topological condition rkH4(X,Z) = 1, which follows from the Lefschetz theorem in the case when the 3-fold X is smooth. We prove the factoriality of the 3-fold X in the case when the hypersurface Gk is smooth and |Sing(X)| ≤ (n+k)(n−1) 5 .
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