Matrix factorization and the generic plane projection of curve a singularity

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 $X$.