On the generic injectivity of Hessian maps of ternary forms

We study the problem of the generic injectivity of the Hessian map, associating with a proportionality class of a ternary form the class of its Hessian determinant, conjectured by C. Ciliberto and G. Ottaviani and recently proved by the same authors. Taking into account that the Hessian curve is the ramification divisor associated with the polar map, we perform a study of the problem using a geometric description of the graph of such a map.