An elementary proof that vector bundles on \mathbb P¹ split

2011/11/03 by William F. Sawin, Sawin, William F.
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AG

paper · pdf · doi:10.48550/arxiv.1111.0702

4 pages

openalex publication_date 2011/11/03 · arxiv created 2011/11/05 · arxiv updated 2011/11/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper gives a new elementary proof of the theorem that all vector bundles on \mathbb P¹ 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.

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