Characteristic integrals in 3D and linear degeneracy

Conservation laws vanishing along characteristic directions of a given system of PDEs are known as characteristic conservation laws, or characteristic integrals. In 2D, they play an important role in the theory of Darboux-integrable equations. In this paper we discuss characteristic integrals in 3D and demonstrate that, for a class of second-order linearly degenerate dispersionless integrable PDEs, the corresponding characteristic integrals are parametrised by points on the Veronese variety.