Generalized Bianchi identities in gauge-natural field theories and the curvature of variational principles

By resorting to Noether's Second Theorem, we relate the generalized Bianchi identities for Lagrangian field theories on gauge-natural bundles with the kernel of the associated gauge-natural Jacobi morphism. A suitable definition of the curvature of gauge-natural variational principles can be consequently formulated in terms of the Hamiltonian connection canonically associated with a generalized Lagrangian obtained by contracting field equations.