Factorial hypersurfaces

TL;DR

This paper estimates the codimension of the complement of factorial hypersurfaces of degree d in projective space for certain degrees and dimensions, contributing to the understanding of the structure of these hypersurfaces.

Contribution

It provides new bounds on the codimension of non-factorial hypersurfaces in projective space for degrees d ≥ 4 and dimensions N ≥ 7.

Findings

Estimated codimension bounds for factorial hypersurfaces

Extended understanding of hypersurface structure in algebraic geometry

Applicable for degrees d ≥ 4 and dimensions N ≥ 7

Abstract

In this paper the codimension of the complement to the set of factorial hypersurfaces of degree $d$ in ${\mathbb P}^N$ is estimated for $d\geqslant 4$, $N\geqslant 7$.