Secant Dimensions of Minimal Orbits: Computations
and Conjectures
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 non-defectiveness of certain higher
secant varieties.
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