Fibr\'e vectoriel de 0-corr\'elation pond\'er\'e sur l'espace $P^{2n+1}$

TL;DR

This paper introduces a new family of stable algebraic symplectic vector bundles on complex projective spaces, analyzing their invariance under deformation and cohomological stability conditions.

Contribution

It presents a novel class of stable symplectic vector bundles on $P^{2n+1}$, extending classical null correlation bundles and examining their deformation invariance.

Findings

New stable algebraic symplectic vector bundles constructed

Bundles are invariant under miniversal deformation

Cohomological conditions for stability established

Abstract

We study in this paper a new family of stable algebraic symplectic vector bundles of rank $ 2n $ on the complex projective space $P^{2n+1}$ whose classical null correlation bundles belongs. We show that these bundles are invariant under a miniversal deformation. We also study the sufficient cohomological conditions for a symplectic vector bundle on a projective variety to be stable.