Generic identifiability of pairs of ternary forms

Abstract

We prove that two general ternary forms of degrees cle d are simultaneously identifiable only in the classical cases (c,d)=(2,2) and (c,d)=(2,3). We translate the problem into the study of a certain linear system on a projective bundle on the plane, and we apply techniques from projective and birational geometry to prove that the associated map is not birational.