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We define the Weyl cycles on X_n^ s , the blown-up projective space P^n in s points in general position. In particular, we focus on the Mori Dream spaces X3 7 and X4 8, where we classify all the Weyl cycles of codimension two. We further introduce the Weyl expected dimension for the space of global sections of any effective divisor that generalizes the linear expected dimension of [ 2] and the secant expected dimension of [ 4].more » « less
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