On the geometry of field-theoretic Gerstenhaber structures

Field-theoretical models with first order Lagrangian can be formulated in a covariant Hamiltonian formalism. In this article, the geometrical construction of the Gerstenhaber structure that encodes the equations of motion is explained for arbitrary fibre bundles. Special emphasis has been put on naturality of the constructions. Further, the treatment of symmetries is explained. Finally, the canonical field theoretical 2-form is obtained by pull-back and integration of the polysymplectic form over space like hypersurfaces.