Studying the Higgs Potential at the e+e- Linear Collider

The determination of the shape of the Higgs potential is needed to complete the investigation of the Higgs profile and to obtain a direct experimental proof of the mechanism of electro-weak symmetry breaking. This can be achieved, at a linear collider, by determining the Higgs triple self-coupling g_HHH in the processes e+e--> HHZ and HHnunu and, possibly, the quartic coupling. This paper summarises the results of a study of the expected accuracies on the determination of g_HHH at a TeV-class LC and at a multi-TeV LC. The statistical dilution arising from contributions not sensitive to the triple Higgs vertex, can be reduced by means of variables sensitive to the kinematics and the spin properties of the reactions.