Factorial hypersurfaces in P^4 with nodes

TL;DR

This paper proves that certain nodal hypersurfaces in four-dimensional projective space are factorial if they have a limited number of nodes, specifically for degrees 5, 6, and 7.

Contribution

It establishes factoriality criteria for nodal hypersurfaces in P^4 with a bound on the number of nodes for degrees 5, 6, and 7.

Findings

Factoriality holds for hypersurfaces with up to (n-1)^2-1 nodes for degrees 5, 6, 7

Provides bounds on the number of nodes ensuring factoriality in P^4

Advances understanding of singularities in hypersurfaces

Abstract

We prove that for n= 5, 6, 7, a nodal hypersurface of degree n in P^4 is factorial if it has at most (n-1)^2-1 nodes.