Chordal varieties of Veronese varieties and catalecticant matrices

Preprint

30 April 1998

preprint
Published by arXiv in arXiv

https://doi.org/10.48550/arXiv.math/9804141

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.

Keywords

CATALECTICANT VARIETIES
CATALECTICANT MATRICES
CHORDAL VARIETY
CATALECTICANT
VARIETY V_D
HOMOGENEOUS
VARIETIES
MATRICES
VERONESE

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