Torsion-free rank one sheaves over del Pezzo orders

TL;DR

This paper proves that torsion-free rank one modules over del Pezzo orders on the projective plane can be deformed into locally free modules, advancing understanding of module deformation in noncommutative algebraic geometry.

Contribution

It establishes the deformation from torsion-free to locally free modules over del Pezzo orders, a novel result in the study of noncommutative algebraic surfaces.

Findings

Torsion-free rank one modules can be deformed into locally free modules.

Deformation results hold specifically for del Pezzo orders on the projective plane.

Enhances understanding of module structure over noncommutative surfaces.

Abstract

Let A be a del Pezzo order on the projective plane over the field of complex numbers. We prove that every torsion-free A-module of rank one can be deformed into a locally free A-module of rank one.