On factoriality of threefolds with isolated singularities

TL;DR

This paper explores conditions under which three-dimensional algebraic varieties with isolated singularities are factorial, focusing on complete intersection threefolds with ordinary multiple points.

Contribution

It provides new sufficient conditions for factoriality of threefolds with isolated singularities, advancing understanding of their geometric properties.

Findings

Identified criteria ensuring factoriality of certain threefolds.

Characterized the types of singularities compatible with factoriality.

Extended previous results on factoriality to broader classes of threefolds.

Abstract

We investigate the existence of complete intersection threefolds $X \subset \mathbb{P}^n$ with only isolated, ordinary multiple points and we provide some sufficient conditions for their factoriality.