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Chordal varieties of Veronese varieties and catalecticant matrices

Vassil Kanev
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Abstract

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.

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Vassil Kanev. 1998-04-30. Chordal varieties of Veronese varieties and catalecticant matrices. https://arxiv.org/abs/math/9804141

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