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Higher secants of spinor varieties
Let be the even pure spinors variety of a complex vector space of
even dimension endowed with a non degenerate quadratic form and let
be the -secant variety of . We decribe a probabilistic
algorithm which computes the complex dimension of . Then, by
using an inductive argument, we get our main result: has the
expected dimension except when . Also we provide theoretical
arguments which prove that has a defective 3-secant variety and has
defective 3-secant and 4-secant varieties.Comment: 23 page
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