  It is proved that the chordal variety of the Veronese variety v_d(P^n) is
projectively normal, arithmetically Cohen-Macaulay and its homogeneous ideal is
generated by the 3 x 3 minors of two catalecticant matrices. These results are
generalized to the catalecticant varieties Gor_{\leq}(T) with t_1 = 2. We also
give a simplified proof of a theorem of O. Porras about the rank varieties of
symmetric tensors.
