Matrix factorization and the generic plane projection of curve a singularity

TL;DR

This paper investigates matrix factorizations associated with generic plane projections of curve singularities in three-dimensional complex space, exploring their relationships with plane curve singularities and the family of space curve singularities.

Contribution

It introduces a study of matrix factorizations derived from generic plane projections of curve singularities and examines their connection to space curve singularities with a given plane projection.

Findings

Characterization of matrix factorizations for generic plane projections

Relationship between space curve singularities and their plane projections

Framework for analyzing matrix factorizations in singularity theory

Abstract

We study the matrix factorizations defined by the generic plane projections of a curve singularity of $\mathbb{C}^3$. On the other hand, given a plane curve singularity $Y\subset \mathbb{C}^2$ we study the family of matrix factorizations defined by the space curve singularities $X\subset \mathbb{C}^3$ such that $Y$ is the generic plane projection of $X$.