Factorial threefold hypersurfaces

TL;DR

This paper proves that certain hypersurfaces in projective 4-space with limited isolated double points are factorial, extending understanding of their algebraic structure and singularity behavior.

Contribution

It establishes factoriality of hypersurfaces with a bound on the number of isolated ordinary double points, a new result in algebraic geometry.

Findings

Hypersurfaces with at most $(d-1)^2 - 1$ singular points are factorial.

Factoriality holds for hypersurfaces with limited isolated ordinary double points.

Provides conditions under which hypersurfaces in $\

Abstract

Let $X$ be a hypersurface in $\mathbb{P}^{4}$ of degree $d$ that has at most isolated ordinary double points. We prove that $X$ is factorial in the case when $X$ has at most $(d-1)^{2}-1$ singular points.