On the non-existence of orthogonal instanton bundles on P^(2N+1)

TL;DR

This paper proves the non-existence of orthogonal instanton bundles on odd-dimensional projective spaces by introducing a new representation of an existing invariant, advancing understanding in algebraic geometry.

Contribution

It establishes a non-existence result for orthogonal instanton bundles on P^(2n+1) and introduces a novel method for representing related invariants.

Findings

Orthogonal instanton bundles do not exist on P^(2n+1).

A new representation of the Costa-Ottaviani invariant is proposed.

The proof relies on properties of rank 2n instanton bundles.

Abstract

In this paper we prove that there do not exist orthogonal instanton bundles on P^(2n+1) . In order to demonstrate this fact, we propose a new way of representing the invariant, introduced by L. Costa and G. Ottaviani, related to a rank 2n instanton bundle on P^(2n+1) .