Chordal varieties of Veronese varieties and catalecticant matrices

Details Chordal varieties of Veronese varieties and catalecticant matrices Chordal varieties of Veronese varieties and catalecticant matrices

1998-04-30

arxiv.org/abs/math/9804141v1

Mathematics

Algebraic Geometry

17 pages, Latex2e

Scientific paper

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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