Experimental Mathematics

Secant Dimensions of Minimal Orbits: Computations and Conjectures

Karin Baur, Jan Draisma, and Willem A. de Graaf

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Abstract

We present an algorithm for computing the dimensions of higher secant varieties of minimal orbits. Experiments with this algorithm lead to many conjectures on secant dimensions, especially of Grassmannians and Segre products. For these two classes of minimal orbits we give a short proof of the relation---known from the work of Ehrenborg, Catalisano--Geramita--Gimigliano, and Sturmfels--Sullivant---between the existence of certain codes and nondefectiveness of certain higher secant varieties.

Article information

Source
Experiment. Math., Volume 16, Issue 2 (2007), 239-251.

Dates
First available in Project Euclid: 7 March 2008

Permanent link to this document
https://projecteuclid.org/euclid.em/1204905879

Mathematical Reviews number (MathSciNet)
MR2339279

Zentralblatt MATH identifier
1162.14038

Subjects
Primary: 14N05: Projective techniques [See also 51N35]
Secondary: 14Q15: Higher-dimensional varieties 14L35: Classical groups (geometric aspects) [See also 20Gxx, 51N30]

Keywords
Projective techniques higher-dimensional varieties classical groups

Citation

Baur, Karin; Draisma, Jan; de Graaf, Willem A. Secant Dimensions of Minimal Orbits: Computations and Conjectures. Experiment. Math. 16 (2007), no. 2, 239--251. https://projecteuclid.org/euclid.em/1204905879


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