Stable real algebraic vector bundles over a Klein bottle

TL;DR

This paper classifies all stable real algebraic vector bundles over a specific type of real algebraic curve, namely a genus one curve without real points, providing a comprehensive understanding of their structure.

Contribution

It provides a complete classification of stable real algebraic vector bundles over a genus one curve without real points, a problem not previously fully addressed.

Findings

Complete classification of stable real algebraic vector bundles over the given curve

Identification of isomorphism classes for these bundles

Insights into the structure of vector bundles over real algebraic curves

Abstract

Let X be a geometrically connected smooth projective curve of genus one, defined over the field of real numbers, such that X does not have any real points. We classify the isomorphism classes of all stable real algebraic vector bundles over X.