Truncated modules and linear presentations of vector bundles

TL;DR

This paper introduces a novel method for constructing linear spaces of matrices with constant rank using truncated cohomology modules and Artinian modules, offering new examples and perspectives in the study of vector bundles.

Contribution

The paper presents a new approach leveraging truncated cohomology and Artinian modules to generate and analyze linear spaces of matrices of constant rank.

Findings

Produced new examples of matrices with constant rank

Provided an alternative perspective on existing constructions

Enhanced understanding of vector bundle cohomology in matrix theory

Abstract

We give a new method to construct linear spaces of matrices of constant rank, based on truncated graded cohomology modules of certain vector bundles as well as on the existence of graded Artinian modules with pure resolutions. Our method allows one to produce several new examples, and provides an alternative point of view on the existing ones.