Weyl cycles on the blow-up of P4 at eight points

We define the Weyl cycles on Xns, the blown-up projective space Pn in s points in general position. In particular, we focus on the Mori Dream spaces X^3_7 and X^4_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 and the secant expected dimension.