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Let X ⊂ P be an integral and non-degenerate m-dimensional variety defined over R. For any P ∈ P(R) the real X-rank rX,R(P ) is the minimal cardinality of S ⊂ X(R) such that P ∈ 〈S〉. Here we extend to the real case an upper bound for the X-rank due to Landsberg and Teitler.

On the real X-ranks of points of Pn(R) with respect to a real variety X ⊂ Pn