The cone of Betti tables over three non-collinear points in the plane

TL;DR

This paper characterizes the cone of Betti tables for modules over the coordinate ring of three non-collinear points in the projective plane, providing a comprehensive description of their algebraic invariants.

Contribution

It offers a complete description of the Betti table cone for modules over the specific coordinate ring, extending understanding of their algebraic structure.

Findings

Describes the cone of Betti tables for modules over three non-collinear points

Provides the Betti cone for finite length modules

Advances the classification of algebraic invariants in projective geometry

Abstract

We describe the cone of Betti tables of all finitely generated graded modules over the homogeneous coordinate ring of three non-collinear points in the projective plane. We also describe the cone of Betti tables of all finite length modules.