Matrices of linear forms of constant rank from vector bundles on projective spaces

We consider the problem of constructing matrices of linear forms of constant rank by focusing on the associated vector bundles on projective spaces. Important examples are given by the classical Steiner bundles, as well as some special (duals of) syzygy bundles that we call Drezet bundles. Using the classification of globally generated vector bundles with small first Chern class on projective spaces, we are able to describe completely the indecomposable matrices of constant rank up to six; some of them come from rigid homogeneous vector bundles, some other from Drezet bundles related either to plane quartics or to instanton bundles on P3.(c) 2023 Elsevier Inc. All rights reserved.

Automated summary

This paper discusses the problem of constructing matrices of linear forms of constant rank by focusing on vector bundles on projective spaces. It introduces important examples of classical Steiner bundles and Drezet bundles, and uses the classification of globally generated vector bundles to describe completely the indecomposable matrices of constant rank up to six.