Vector bundles over noncommutative nodal curves

TL;DR

This paper studies vector bundles over specific noncommutative curves, providing classifications for certain types and demonstrating the complexity of the problem in more general cases.

Contribution

It classifies vector bundles over noncommutative nodal curves of string and almost string type, and shows the classification problem is wild in other cases.

Findings

Classification is possible for string and almost string types.

In other cases, the classification problem is wild and intractable.

Provides a framework for understanding vector bundles in noncommutative geometry.

Abstract

We desribe vector bundles over a class of noncommutative curves, namely, over noncommutative nodal curves of string type and of almost string type. We also prove that in other cases the classification of vector bundles over a noncommutative curve is a wild problem.