Betti tables for indecomposable matrix factorizations of $XY(X-Y)(X-\lambda Y)$

TL;DR

This paper classifies the Betti tables of indecomposable graded matrix factorizations over a specific elliptic singularity using the theory of weighted projective lines, advancing understanding in algebraic geometry and singularity theory.

Contribution

It provides a complete classification of Betti tables for indecomposable matrix factorizations over the simple elliptic singularity $f____$, utilizing weighted projective line techniques.

Findings

Classification of Betti tables for the given singularity.

Connection between matrix factorizations and weighted projective lines.

Enhanced understanding of indecomposable objects in singularity categories.

Abstract

We classify the Betti tables of indecomposable graded matrix factorizations over the simple elliptic singularity $f_\lambda = XY(X-Y)(X-\lambda Y)$ by making use of an associated weighted projective line of genus one.