Chordal varieties of Veronese varieties and catalecticant matrices
Abstract
It is proved that the chordal variety of the Veronese variety vd(Pn) 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≤(T) with t1 = 2. We also give a simplified proof of a theorem of O. Porras about the rank varieties of symmetric tensors.
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