Chordal varieties of Veronese varieties and catalecticant matrices

It is proved that the chordal variety of the Veronese variety is projectively normal, arithmetically caulay, and its homogeneous ideal is generated by the 3×3 minors of two catalecticant matrices. Results are generalized to the catalecticant varieties Gor_≤(T) witht ₁=2. Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory. Vol. 56. Algebraic Geometry-9, 1998.