An elementary proof that vector bundles on $\mathbb P^1$ split

TL;DR

This paper presents a new elementary proof demonstrating that all vector bundles on the projective line split into direct sums of line bundles, simplifying the understanding of their structure.

Contribution

It introduces an elementary proof based on divisors associated with germs of sections, offering a simpler approach compared to previous methods.

Findings

All vector bundles on $\\mathbb{P}^1$ split into line bundles

The proof is elementary and relies on divisor analysis

Provides a new perspective on vector bundle splitting

Abstract

This paper gives a new elementary proof of the theorem that all vector bundles on $\mathbb P^1$ split into the direct sum of line bundles. The proof is based on the study of divisors associated to germs of sections at the generic point.