Fibr\'e vectoriel de rang $2n+1$ sur l'espace $\mathbb{P}^{2n+2}$

TL;DR

This paper constructs new families of algebraic vector bundles of rank 2n+1 on complex projective spaces by extending lower-rank bundles using Kumar-Peterson-Rao's method, including a novel rank 3 example on .

Contribution

It introduces new vector bundles of rank 2n+1 on n+2 from known bundles on n+1, and provides a unique rank 3 bundle example different from previous constructions.

Findings

New families of vector bundles of rank 2n+1 on n+2.

Construction of a novel rank 3 bundle on .

Application of Kumar-Peterson-Rao method to generate these bundles.

Abstract

We build in this article new families of algebraic vector bundles of rank $2n+1 $ on the complex projective space $\mathbb{P}^{2n +2} $ from two bundles of rank $2n$ on $\mathbb{P}^{2n+1}$, the weighted null correlation bundles \cite{bah2} and the weighted Tango bundles \cite{bah1} while using the method of Kumar-Peterson-Rao \cite{ku-ra-pe}. We construct another example of vector bundle of rank 3 on $\mathbb{P}_\mathbb{K}^4$ different than the one presented in \cite{ku-ra-pe}, where $\mathbb{K}$ is any field.