Equations for secant varieties of Veronese and other varieties

Details Equations for secant varieties of Veronese and other varieties Equations for secant varieties of Veronese and other varieties

2011-11-19

arxiv.org/abs/1111.4567v1

Mathematics

Algebraic Geometry

34 pages, to appear in Annali di Matematica Pura e Applicata, this paper merges and supersedes the papers arXiv:1006.0180 and

Scientific paper

New classes of modules of equations for secant varieties of Veronese varieties are defined using representation theory and geometry. Some old modules of equations (catalecticant minors) are revisited to determine when they are sufficient to give scheme-theoretic defining equations. An algorithm to decompose a general ternary quintic as the sum of seven fifth powers is given as an illustration of our methods. Our new equations and results about them are put into a larger context by introducing vector bundle techniques for finding equations of secant varieties in general. We include a few homogeneous examples of this method.

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