Factoriality of complete intersection threefolds

TL;DR

This paper proves that certain complete intersection threefolds in projective space are factorial if they have a limited number of nodal singularities, extending understanding of their algebraic structure.

Contribution

It establishes a new criterion linking the number of nodal singularities to factoriality in complete intersection threefolds.

Findings

Factoriality holds if the number of singular points is below a specific threshold.

The threshold for singular points depends on the degrees n and k of the hypersurfaces.

The result applies to threefolds with smooth F_k and nodal singularities.

Abstract

Let X be a complete intersection of two hypersurfaces F_n and F_k in the projective space P^5 of degree n and k respectively with n >= k, such that the singularities of X are nodal and F_k is smooth. We prove that if the threefold X has at most (n+k-2)(n-1)-1 singular points, then it is factorial.