Generalized wahl maps and adjoint line bundles on a general curve

For any two line bundles on a smooth curve, there are so called Wahl maps, that can be viewed as generalizations of the ordinary Gaussian. These maps govern various properties of the projective embeddings of C, like for example the first order deformations of the projective cone that smooth the vertex. In this paper we investigate these maps from the point of view of the intrinsic geometry of C, by applying an approach of Voisin for the case L = N = K