Veronese webs for bihamiltonian structures of higher corank

TL;DR

This paper extends the concept of bihamiltonian structures to a broader class and introduces a generalized Veronese web as a local invariant, with examples illustrating the new theory.

Contribution

It generalizes the notion of Veronese webs for bihamiltonian structures of higher corank beyond the classical case.

Findings

Extended bihamiltonian structures to a wider class.

Introduced a generalized Veronese web as an invariant.

Provided examples demonstrating the new framework.

Abstract

It is shown how the well-known class of bihamiltonian structures in general position can be extended to a wider class. A generalization of the corresponding notion of a Veronese web for this wider class is presented (in the general position case Veronese webs form complete systems of local invariants for bihamiltonian structures). Some examples are considered.